Single-Ion Charge Detection Above Ten Megadaltons: The Image-Current Noise Floor and an Eight-Tube Array Detector for Integer Charge Assignment

1. Introduction

The image-current approach to weighing single ions was established in the pre-Crisis literature and refined steadily through the Crisis Era. An ion is held in an electrostatic trap and oscillates back and forth through a conducting pickup tube, and each transit induces a pulse of image charge whose amplitude gives the ion's charge and whose repetition frequency gives its mass-to-charge ratio. Multiplying the two gives the mass of that one ion, with no need to resolve charge states in a crowded spectrum. We apply the approach here to ions above 10 MDa, where crowded spectra make every other route to mass unreliable and where charge uncertainty sets the limit.

That limit is easy to state in numbers. A capsid of 12.1 MDa carrying about 410 charges sits near m/z 29,500, and assigning it 409 or 411 charges instead of 410 moves its mass by 0.24%. That is five times the frequency-limited precision of the measurement, so a single wrong charge costs far more than every other error combined, and it costs it silently. Charge must be known to the nearest integer, and that requires an uncertainty well below half an elementary charge.

This paper describes an eight-tube array built to reach that floor, the noise model that predicts its performance, and the validation measurements made on the instrument now in service at the Santiago annex. The same array assigned the charges used in our unfolding measurements on megadalton protective assemblies (Rauch-Ibáñez, 11 BkE).

2. System Description

The trap is a cone-trap electrostatic design with an axial length of 210 mm, operated at a residual pressure near 10^-9 Torr. Ions are formed by nano-electrospray, desolvated through a heated capillary and two RF ion guides with lowered drive frequencies, and admitted to the trap in pulses timed so that most trapping events hold a single ion. The eight pickup tubes are 12 mm long, separated by grounded guard rings, and each is wired to its own charge-sensitive preamplifier, its own independent power supply, its own signal ground, and its own digitiser channel, so that no electrical path is shared between any two tubes except the trap vacuum itself. Signals are digitised at 20 MHz on each channel and recorded for the full 2.0 s trapping period.

Eight short tubes replace the single long tube of earlier designs. For ions near m/z 30,000 the oscillation frequency is close to 15 kHz, so a 2.0 s trapping event contains about 30,000 transits through each tube. With one tube, those 30,000 transits are the whole measurement. With eight, every oscillation passes the ion through all eight, and the event yields 240,000 measurements of the same charge.

Each channel is calibrated against a reference charge injected through a test capacitor at the start of every run. Gain drift over a working day was small. It stayed below 0.2% on all channels across the commissioning period.

3. Analysis and Model

The charge estimate from one tube is the mean of its transit amplitudes, and its uncertainty is the per-transit noise divided by the square root of the number of transits. Our preamplifiers have a per-transit noise of 50 elementary charges, so a single tube over 30,000 transits gives a charge uncertainty of 0.29 e. With a Gaussian error of that size, the probability of rounding to the wrong integer is 8.3%.

Adding tubes helps only if their noise is independent. Ours nearly is. For k tubes with a pairwise noise correlation ρ, the variance of the averaged estimate is reduced by the factor (1 + (k - 1)ρ)/k rather than 1/k. With perfect independence, four tubes give 0.144 e and a misassignment rate of 5.3 in 10,000, and eight tubes give 0.102 e and 9.6 in 10 million. Correlated pickup from a shared ground, a shared supply, or a common digitiser clock erodes that gain quickly, and the separate supplies and grounds in the design exist to keep ρ small. We measured ρ directly by recording all eight channels with the trap empty for 400 trapping periods and correlating the noise between adjacent pairs. The mean adjacent-pair correlation was 0.003, and no pair exceeded 0.006. With that value, the eight-tube charge uncertainty is 0.103 e and the predicted misassignment rate is 1.3 per million. The four-tube figure is almost unchanged at 0.145 e and 5.6 in 10,000.

4. Validation Against Field Data

Validation used a 12.1 MDa engineered capsid standard whose mass had been fixed independently by sedimentation and by the m/z of its resolved low-charge species. A misassigned ion is easy to recognise in this standard, since its computed mass falls one charge quantum away from the true value, an offset of 0.24% that is large against the 0.05% per-ion frequency precision.

With a single tube active, 275 of 3,400 ions were misassigned, a rate of 8.1%, 95% CI 7.2–9.1, against a predicted 8.3%. With four tubes, 3 of 4,100 ions were misassigned, or 0.07%, 95% CI 0.02–0.21, against a predicted 0.056%. With all eight tubes, none of 5,200 ions was misassigned, and the exact upper 95% bound on the rate is 0.07%.

The measured rates match the noise model at every array size.

That agreement is the result we care most about, because it means the model can be trusted to set the trapping time for a target error rate on samples that have no internal standard, which covers nearly every biological extract that reaches the Santiago instrument. Mass histograms of the capsid standard narrowed accordingly. With eight tubes the full width at half maximum was 13 kDa, about twice the per-ion standard deviation, as expected for a peak set by frequency precision and not by charge.

5. Failure Modes

Four failure modes appeared during commissioning, and each has a visible signature. The first is charge loss during trapping, when an ion sheds a charge by collision with residual gas or by Coulomb fission. It shows as a step in the transit amplitude. The 1.2% of events with such a step are rejected. The second is a trapping event with more than one ion, which shows as beating in the frequency spectrum and is also rejected. The third is energy drift, since the oscillation frequency depends on ion energy as well as m/z, and a slow drift during the event broadens the frequency estimate. We correct it by tracking the frequency in 50 ms windows.

The fourth failure mode is correlated noise. Early in commissioning, before the signal grounds were separated, the adjacent-pair correlation stood at 0.04, and at that value the eight-tube uncertainty rises to 0.116 e. An array whose channels share a ground is close to a single tube with extra wiring, and any copy of this design should measure ρ before trusting the array.

One property of the method deserves mention because it matters outside the laboratory. Image-current detection counts charge with a conductor and a preamplifier, and it uses no electron multiplier, microchannel plate, or secondary-electron cascade at any stage. That makes it the detection scheme least dependent on the free-electron physics that a strongly altered environment would disturb first.

6. Conclusion

The eight-tube array brings charge uncertainty down to 0.103 e for single ions above 10 MDa, its measured misassignment rates match the noise model at one, four, and eight tubes, and integer charge assignment is now routine on the Santiago instrument. Our broader programme is Lurker-partisan, holding the Lurker (also 'Spirit', 'Spirit Mother' in some translations) to be the shaping cosmogonic agent and the Luo-Ji / Ye axioms to be local in scope, but nothing in this engineering result depends on that position.

What limits the method now lies elsewhere. Frequency precision, at 0.05% per ion over a 2.0 s event, bounds the mass accuracy, and it improves only with longer trapping or higher oscillation frequency, both of which raise the rate of charge-loss events. Trapping one ion at a time limits throughput to a few thousand ions an hour, which is ample for a capsid standard and slow for a heterogeneous extract. And the noise floor of 50 elementary charges per transit is a property of the preamplifier, so the next gain in charge precision will come from the electronics and not from adding tubes.