Mass and Charge Measurements on Heavy Ions

The relationship between mass and charge has been a crucial topic in mass spectrometry (MS) because the mass itself is typically evaluated based on the m/z ratio. Despite the fact that this measurement is indirect, a precise mass can be obtained from the m/z value with a high m/z resolution up to 105 for samples in the low mass and low charge region under 10,000 Da and 20 e, respectively. However, the target of MS has recently been expanded to the very heavy region of Mega or Giga Da, which includes large particles and biocomplexes, with very large and widely distributed charge from kilo to Mega range. In this region, it is necessary to evaluate charge and mass simultaneously. Recent studies for simultaneous mass and charge observation and related phenomena are discussed in this review.


INTRODUCTION
In the study of mass spectrometry (MS), almost all information is obtained through the ratio of m/z. It is typically di cult to obtain mass and charge independently. For example, M + and M 2 2+ are recognized as the same species in mass spectra. 1,2) However, in terms of ions with a smaller charge, it is possible to speculate each amount. ose multiply charged species (M 2 2+ ) appears as a series of peaks involving (M+2H 2 ) 2+ and M 3 2+ for example between those of singly charged ions. e intensities of each charge state show di erent dependences on conditions of ionization and sampling.
As a result, speculation is only possible when the resolution of MS is su cient to resolve the m/z ratio of every ion and if its charge is relatively low. Recently ultrahigh mass species, such as biocomplexes, particles, cells, and viruses have been gradually incorporated into the scope of MS. [3][4][5] For those species, the charge and its distribution are large and the m/z resolution is not su ciently high to permit perfect resolution so that their mass cannot be determined only by observing m/z. Some a combination of techniques such as ion mobility spectrometry (IMS) or the simultaneous observation of mass and charge so called charge detection mass spectrometry (CDMS) are indispensable. Here we report recent progress made in IMS combined MS (IMS/MS), tandem IMS, and CDMS, especially for particles and large molecules to obtain their actual mass and charge.
Mass and charge simultaneous observations have been performed since Millikans' historical work. 6,7) Even in this very early stage of studies concerning elementary particles, a simultaneous measurement was crucial. His historical works can be viewed as a simultaneous measurement of charge, gravity, and mobility on a single particle. It is signi cant that the m/z of an electron was already determined before Millikans' studies. 8) e fact shows that the determination of each of mass and charge is more di cult than that for m/z. However once the elementary charge was determined, the m/z of ions is almost equivalent to their mass itself with their speculated charge. is is one of the reasons why MS is widely accepted as a basic identi cation method. e method was developed in order to detect "di erences" between samples and to resolve "complicated mixtures" with a high-resolution and a high-sensitivity. From this point of view the charge distribution must be reduced to unity or to a low a value as possible. e m/z resolution has been enhanced to as high as 10 5 but a similar level has not been accomplished in terms of the charge as well as mass resolution itself. e target of MS has now been extended to ultrahigh mass species, as mentioned above, for large biocomplexes and particles, where a large charge of around 100 e is on the molecule with a mass of around 1 MDa. 9,10) In this mass region, it is not su cient to identify them with only based on m/z values. Other techniques such as IMS must also be employed. 9,10) Another approach is to determine the charge directly or indirectly. Recent progress on detection devices enables us to perform simultaneous measurements on molecules or particles in terms of m/z value and charge or kinetic energy. 1,4,5,11,12) For those measurements, ionization and detection methods are also important. It is di cult to desorb larger molecules and particles into a vacuum or gas and to detect them as their mass and size increase. ose species have strong adhesive forces arising from van der Waals interactions between wide at contact areas, which prevent them from being desorbed. eir detection e ciency also is degraded because the electron multiplier, 13,14) the most common and e ective detector, has diminished detection e ciency for low speed heavy ions. Not only detection e ciency but also manipulating the movement of those ions is a signi cant problem.
ermal energy and gravity are comparable to the kinetic energy of ions that are electronically accelerated when their m/z is high.
To treat larger species with MS, methods for the ionization of larger charges, enhanced detection methods, separation or identi cation methods have been in continuous development. Several of these achievements have been made: CDMS and IMS related measurements. Both methods utilize not only a sensitive electron multiplier but also low sensitive detection methods such as a charge detector and a condensation particle counter. 15) Despite their low e ciency, throughput, and sensitivity, those methods have many advantages, especially for larger species over electron multipliers that are used in conventional MS. ese current technical progresses and observed phenomena are reviewed here.

EXPERIMENTAL TECHNIQUES
Experimental techniques have been developed to handle heavy ions. We summarize these techniques in terms of ionization, separation, and detection below.

Ionization methods Conventional methods
Many ionization methods have been developed for use in conjunction with MS so far. ere are several problems associated with ionizing heavy and large molecules: large charge, desorption, so ionization, and constant ionization e ciency. Laser desorption ionization (LDI) and matrix-assisted LDI (MALDI) are among the most suitable methods for ionizing samples with low volatility and with a very small amount such as a spot. Especially MALDI with the indirect ionization mechanism makes it possible to produce intact ions derived from large biomolecules. 16) However the charge is usually restricted to unity. It is very di cult to produce multiply charged ions by MALDI. 17) e detection e ciency for heavy molecules decreases as their mass increases when their charge is restricted to be low. 13) e results show that the ion detection e ciency is not unity, even in the relatively low m/z region under 10 4 . For very large biocomplexes or particles, MALDI may not be appropriate in terms of the amount of charge. Not only the charge, but also the ionization e ciency dependence on the matrix 2,18) and ne molecular structure 19,20) are also serious problems. ere are many elds where the e ciency needs to be constant for all samples. To minimize the matrix effect, for example, a femtosecond laser has been utilized for elementary analyses. 18) Electrospray ionization (ESI) has also been shown to be a powerful method for ionizing especially biomolecules in very "so " conditions. 21,22) Multiply charged ions are e ectively produced by the method with highly sensitive detection even in high-mass region because of their reduced m/z with the high charge. Recently ultrahigh mass proteins, 9,10,23) nano or micrometer droplets of water or ethylene glycol, [24][25][26][27] polymers, 28,29) submicrometer polystyrene particles, 30,31) and even viruses [32][33][34] have also been produced by ESI and have been detected by MS and IMS with high charge up to 10 6 e. Especially sonic spray a sort of spray technique with an electric eld and a gas ow can also produce highly charged triethylene micrometer particles. 35) ESI thus has already realized the production of highly charged large and heavy molecules and particles. However charge and polarity are closely related to solution conditions such as pH and solvent. 2) It is necessary to control the conditions for some selected targets so as to generate sucient charge. e large charge distribution accompanied by the large charge o en makes it di cult to identify the mass of the samples only by m/z values. Handling of insoluble and trace amounts of samples on a tiny spot are also serious problems of ESI. 23)

Laser induced acoustic desorption ionization
Laser-induced acoustic desorption ionization (LIAD) is a method that attempts to solve the above mentioned problems. [36][37][38][39][40][41][42][43] Figure 1 shows a schematic view of LIAD. A fundamental or a second harmonic YAG laser beam with a relatively high power of 30 mJ/pulse is mildly focused on a sample substrate of sapphire plates separated by a layer of liquid mercury, 36) silicon wafers, [40][41][42][43] foils made of metals such as Fe, Al, and Ti. 37,38) e thickness of the plate is 500 µm for Si wafers and around 10 µm for metal foils. Samples such as cells, viruses, and large particles are deposited on the opposite side of the focus side of the sample plates and are then irradiated by the YAG laser. e power density at the point of focus is around 10 8 to 10 9 W/cm 2 . e laser pulse induces an acoustic pulse that desorbs and ionize the samples on the substrate. e ionization mechanism has not been well understood 36) but the e ciency is strongly dependent on the plate material. 38) Au and Si provide a high signal intensity but Fe does not. Some kinds of charge transfer or polarization between the sample and the plate should play crucial roles. 36,[40][41][42][43] e polarity and the amount of charge of the produced ions are strongly dependent, not only on the sample plate, but also on the samples and the method used in their preparation. For large particles and heavy biomolecules, ions with a large positive charge are mainly produced. 36,43) e laser does not hit the sample directly so that the method is indirect and a very so ionization method that can be ap- plied for biosystems. 40) us indirect ionization, however, also results in a low ionization e ciency. 39,44) Sometimes LIAD is used mainly for desorption followed by post ionization such as electron impact, chemical ionization, and corona discharge. In terms of corona discharge, the charge is enhanced by one or two orders of magnitude. 40) e discharge is produced inside the trap just a er the ion injection from LIAD by applying a high RF eld of 3,000 V pp for one second with the introduction of 50 mTorr of extra He. e discharge is monitored by observing the blue and white plasma light of the discharge and by measuring the charge of by-produced ions. e pressure is optimized in every measurement to achieve e cient ionization. With careful control of the discharge, the charge enhancement procedure is performed so as to not destroy the ions that are trapped.
ose post ionization methods have always been the cause of the destruction of ions but the samples measured in this system are restricted to the large and heavy samples, such as cells which are su ciently durable to hold their structures against the discharge. e produced ions are heavy and their amount and distribution of charge are also large. To identify the sample, the determination of both of charge and m/z is indispensable, which is described in the sections of "Ion Trap" and "Direct Charge Detection."

High-voltage assisted laser desorption ionization
To produce highly charged ions with a laser, high-voltage assisted laser desorption ionization (HALDI) is one of the candidate methods. [45][46][47][48] Multiple charged ions are produced e ectively with HALDI 45) whereas single charged ions are produced in the case of LDI and MALDI. 16,17) In terms of polarity, with LDI and MALDI, both positive and negative ions are produced but the polarity is strongly dependent on the matrix. 2,18) HALDI can control the polarity of the product ions simply by the voltage. 45,46) Another advantage of HALDI is that no matrix is used, which leads to signals without contaminating ions from the matrix. 45) Figure 2 shows a schematic view of HALDI, which consists of an ionization laser, a sample plate, and a highvoltage power supply. A fundamental beam of a YAG laser is used to desorb and ionize sample solutions on the sample plate made of a conductive material such as Au, Al, Ag, and stainless steel, a semiconductive material of Si, and nonconductive one of polytetra uoroethylene (PTFE) where a high-voltage (HV) of several kV of both polarities is applied.
Large biomolecules such as cytochrome c, ubiqutin, and myoglobin are ionized to have large charge over +20 e without any matrix, which are similar to ions produced by ESI, from solutions of the sample in methanol/water (50 : 50, v/v) with 0.1% formic acid. 45,49) Ions are produced only when both the high-voltage and the laser are applied. e signal intensity heavily depends on the laser power used, the HV, the pH of the solution, and the materials of the sample plate. e high-voltage applied to the sample plate produces a high-eld at the laser spot that contributes to the ionization of the sample. In terms of the plate material, no ion is produced with nonconductive PTFE but is produced in the case of semiconductive Si. e authors proposed that some roughness of the plate contributes to the ionization processes. e pH dependence is similar to that of ESI: the average charge number increases from +8 of the methanol/water so-lution without formic acid to around +17 of that with 0.1% formic acid. e method can be considered to be a hybrid method of LDI and ESI with the advantages of both. 45)

Separation Ion trap
An ion trap, which was originally developed to cool down high-energy particles, [50][51][52][53] is now used in MS. 2,4,51,54,55) Various kinds of ion traps have been developed to hold, separate, and break ions. 2,55,56) One of the most common ones is a quadrupole ion trap. Figure 3 shows the structure of the trap for heavy ions 4) with the LIAD ion source described in the previous section, and a charge detector with a Faraday plate that is described in the "Direct Charge Detection" section. e system consists of a quadrupole ion trap, LIAD, the detector with the Faraday plate, and a mesh. e mesh is made of stainless steel with more than a 90% transmission and is placed between the Faraday disc and the exit hole of the ion trap to shield the RF eld of the ion trap. For usual MS, a high-frequency (10 5 to 10 6 Hz) high-voltage (100 to 300 V) (RF) is applied to the center ring-like electrode. To apply the quadrupolar potential, the electrodes have hyperbolic surfaces with minimum distances of r 0 and 0 0 2 z r = in terms of the radius and the axis. e shapes of the electrodes provide an inhomogeneous eld distribution in the trap where the eld near each electrode is strong whereas that further away is weak. At the center of the trap, there is no eld of RF.
When the produced electric eld changes too quickly for the ions to follow, the ions near the electrode gradually move to the place apart from the electrode to avoid the high eld. Finally the ions are trapped at the center of the trap where the eld is lowest. 51,52) e movement of the ions in the trap strongly depends on the m/z of ions and the frequency and voltage of the RF. To hold heavy ions with larger m/z against gravity, a lower frequency and a higher voltage of around 100 Hz and 1 kV are crucial. 4,[40][41][42][43]57) However, when a too low frequency and a too high voltage are applied, ions with low m/z can follow the eld and the amplitude of the movement in the trap is large enough to be ejected from the trap. [51][52][53] is frequency and the voltage dependence is represented mathematically as the stability condition, which is derived from the Mathieu equation: where V and Ω RF is the amplitude and the angular frequency of the RF. When we apply 1,000 V and 200 Hz to the trap with the size of r 0 =10 mm to Eq. (1), the lowest m/z of ions to be held is estimated to be 2.7×10 9 .
Usually m/z scanning is performed by increasing V with a xed Ω RF . e scanning range in this case is limited to three orders of magnitude because of limitations associated with the RF power supply. In contrast, a much wider range of more than ten orders of magnitude is realized by scanning Ω RF . 4) e frequency and the voltage dependence is utilized as m/z separation. For usual ions with low m/z the scanning is performed with increasing RF voltage to eject ions with m/z values from lower to higher. In this m/z region, the frequency tends to be high around 1 MHz where the RF power supply works in the resonant condition with the xed frequency. It is easy to change the RF voltage but not the frequency. For ions with higher m/z, on the other hand, a frequency of around 100 Hz is su ciently low to permit audio electronic devices with broadband characteristic working at nonresonant conditions to be used. 4,[40][41][42][43] e m/z selection to eject from lower to higher m/z can be performed by scanning the frequency from higher to lower. Actually, the m/z separation of heavy ions such as cells, viruses, and large particles is performed with the system in Fig. 3. With the scanning from 350 to 20 Hz with a voltage of several kV, various polystyrene particles, cells, and viruses with m/z from 10 7 to 10 11 can be readily separated. 4,44) Fig. 4. (Le ) Mass spectrum of Jurkat cancer cells. 41) Each peak corresponds to the charged cell with an average mass of 4.6×10 13 Da. e horizontal axis shows a scanning time of a trap RF frequencies from higher to lower, which corresponds to the m/z around 10 9 from lower to higher. e vertical axis shows the voltage of a charge sensitive ampli er described in Fig. 7. e expansion shows a pulse shape of a peak. (Right) Constructed mass and charge histograms of polystyrene particles and Jurkat cancer cell. 41) Reprinted with permission from American Chemical Society. Copyright (2008) American Chemical Society. Figure 4 (le ) shows the observed mass spectrum of Jurkat cancer cells 41) ionized by LIAD with post ionization of the corona discharge, as described in the "Laser Induced Acoustic Desorption Ionization" section. Each peak corresponds to the charged cell. 41) e horizontal axis shows the scanning time of the RF frequencies from higher to lower corresponding to m/z values from lower to higher. e vertical axis shows the voltage of the charge sensitive amplier described in the "Direct Charge Detection" section. e expansion shows a pulse shape. 41) Figure 4 (right) shows the constructed mass and charge histograms for polystyrene particles and Jurkat cancer cells 41) from information regarding each ion on m/z and charge. e procedure to determine mass and charge of each sample is described in the "Direct Charge Detection" section. e obtained average mass and charge are 8.3×10 14 Da and +40,000 e for the polystyrene particles with a diameter of 15 µm and 4.6×10 13 Da and +16,858 e for Jurkat, respectively. e mass of the particle of 8.3×10 14 Da is in good agreement with the expected one of 1.1×10 15 Da. e m/z and mass resolution is evaluated with C 60 and standard polystyrene particles with accurate, prede ned diameters from 50 nm to 3 µm. In the case of C 60 with the RF frequency of 200 kHz in 20 mTorr He, a mass resolution of (m/z)/∆(m/z)≈500 is achieved. 40) Approximately 15,000 singly charged C 60 ions are trapped here detected with the Faraday plate. e m/z and ∆m/z are evaluated by the conversion from frequency to mass with Eq. (1). Figure 5 shows the mass spectra of the standard polystyrene particles with the diameters of 50 and 100 nm. 4) ere are many species with multiple charges and clusters. e horizontal and vertical axes represent m/z and detected charge, respectively. For the singly charged ions m/z is equivalent to m. Apart from Fig. 4 with very few ions of much larger cells and particles, Fig. 5 shows measurements that seem to be performed with many ions, each peak area corresponds to the number of detected ions. e expansions show the peak widths of monomer ions with a single charge. e peak tops appear at 4.12×10 7 and 3.26×10 8 Da, which are in good agreement with the expected values of 4.14×10 7 and 3.31×10 8 Da.
e FWHM widths are 19% and 10% of the corresponding peak top mass for the 50 and 100 nm particles so that the FWHM mass resolutions are estimated to be around 5 and 10. Because the mass distribution of the standard particles are estimated to be around 3% with the narrow diameter distribution of 1%, the observed wide mass distribution must be due to the resolution of this system. us, the obtained much low resolution compared to that of C 60 may not arise from noise of the detection system described in the "Direct Charge Detection" section, because even for much heavier ions with a large charge, the m/z and mass resolution is restricted to be 4 where the noise level is not dependent of the charge of ions. 4,40,41) In these kinds of trap measurements, the pressure in the trap can be a serious problem. Here 20 to 100 mTorr helium bu er gas is used for the heavy ions to dump the initial kinetic energy to hold ions at the center of the trap and to enhance the charge with the corona discharge.
is relatively high-pressure may cause a reduced resolution for heavy ions but for C 60 , it is irrelevant.
ose results show that heavy ions such as cells, viruses, and large particles can be analyzed by MS with a relatively high m/z resolution. However m/z observations are not sufcient to determine mass. e mass of the ions can be only determined by observing m/z and z simultaneously and precisely. In addition, the m/z analysis with high-sensitivity for the heavy ions requires ions with a large charge to detect them as a single molecule and also some special ionization methods such as LIAD with corona discharge. e large charge leads to a large charge distribution and low resolution of the charge measurement, which results in di culties in determining the charge and the mass precisely. e precise determination the charge of a single molecule is still challenging subject to solve. 31,58,59) Ion mobility spectrometry e resolution of MS reaches the level of 10 5 , which is su cient to resolve large biocomplexes up to 1 MDa with tens of e. However the large charge distribution coming from the large charge as described above results in mass spectra that are overlapped and complicated in terms of determining the actual mass. To solve the problem of MS, IMS is now becoming a key technology as a combined system of IMS/MS where IMS works as a structural lter or separator for MS. 2,53,55) IMS can separate the structures of ions through inter- molecular interaction or collision between ions and bu er gas. 2,53,55,60,61) e selection is performed based on mobilities, which closely related to the cross section between ions and bu er gas or their size. e mobility is tightly correlated to m/z values, but is not identical to it. 2,55,60) IMS/MS provides us with so called "two-dimensional" information of m/z and mobility on each ion from which we can deduce the precise mass of ions. For example, M + and M 2 2+ have the same m/z but di erent mobilities because they have di erent structures. 2,53,55) In practice, the collision, which is essential to IMS, causes the di usion or loss of ions and signal intensities. In addition, the collision requires a much higher pressure of bu er gas than that of MS, which leads to di culties in interfacing IMS to MS. Despite of those difculties, there are many IMS systems that can be connected to MS. Here we introduce two types: di erential mobility analyzer (DMA) and traveling wave IMS (TWIMS). Figure 6 shows structures of (a) DMA and (b) TWIMS. Both are commercialized and have many applications. 2,53,55) DMA working at ambient pressure has been used as a lter for aerosol and particles for many years, 61) which selects and passes some ions with a certain mobility. It utilizes two electrodes with an electric eld between them and the presence of a gas ow, and an inlet and an outlet of ions. e introduced ions feel the electric force of the eld and the force of the air ow. e resultant force and the ion mobility dictate the trajectory and the selection of ions inside DMA. Too large or too small ions cannot track the right trajectory to pass through DMA (Fig. 6a). Because DMA functions at ambient pressure basically, the order of measurements are always DMA rst and MS second to follow the gas ow due to the di erence between their working pressures.
TWIMS, on the other hand, was developed by Waters Co., Ltd. 62) to be integrated into MS so that the commercialized system has TWIMS between multiple MS systems. To connect MS systems easily, TWIMS functions at a very low pressure around several hundreds Pa compared to DMA. Figure 6b shows a schematic diagram and the basic concept of the system. e system is equipped with a stacked ring ion guide (SRIG) where a RF (around MHz and several hundreds V) is applied to co-axial ring electrodes to trap ions. Each adjacent electrode of SRIG has an opposite polarity of RF so that intense and high-frequency electric elds are applied between the nearest electrodes. e frequency is so high that the ions cannot follow the polarity change of the RF moving gradually from the inner rim to the center of the SRIG according to the eld strength. e ions then are trapped at the center of the each electrode since the trap potential is cylindrically symmetric with sinusoidal distortion along the center axis. 62) e trap mechanism is similar to that for a quadrupole ion trap. e trapped ion can be easily transported by applying bias voltages along the axis in SRIG. To achieve a higher resolution and high sensitivity, the length of the trap should be long so that the SRIG structure is repeated to extend the length of the trap, which are represented as dotted triangle in Fig. 6. e procedure of TWIMS is shown in Fig. 6b, where a waveform called a travelling wave (TW) is applied to the SRIG electrodes for ion mobility with the superimposed RF for the ion trap. TW is continuous moving waves with a eld of tens of V/cm and a speed of hundreds of m/s, which drives the trapped ions out of the SRIG to be detected by MS. e ions with higher mobility represented by open circles in the gure are e ectively transferred to MS whereas those with smaller ones represented by lled circles are le in the SRIG. us, the mobility is measured by the ejection e ciency in TWIMS. is procedure is crucial for TWIMS where whole ions are utilized for the mobility measurements in contrast to DMA which can only pass selected ions. High sensitivity with a reasonable resolution can be realized by tuning the voltage and the speed of the TW.
TWIMS has achieved high sensitivity with SRIG by applying not only a DC bias but also well-designed RF and TW waveforms. ose waveforms drive the ions with complicated trajectories and the high elds of the waveforms heat up and distort the ions. 62,63) ese e ects make it dicult to convert the observed ejection e ciencies or the time pro le of TWIMS to the actual mobilities. For example, the linear relationship between the mobilities obtained from the TWIMS pro le and the mobilities obtained by other measurement systems is fairly good for rigid and spherical molecules whereas it does not hold for asymmetric or so molecules. 64) By utilizing both systems, it is possible to deduce the mass and charge of heavy biocomplexes and particles with many charges. 9,10,24,25,35) It is very di cult to distinguish heavy ions with many charges from a complicated one dimensional m/z mass spectrum. However the overlapped peaks in the spectrum can be separated in the two dimensional mass-mobility spectrum. e mass, charge, and also structure of the heavy ions with up to 1 MDa and around 100 e are determined precisely. 9,10) ose commercialized systems contribute to the rapid development of heavy biocomplexes with their structural and functional analyses. ere is an essential problem associated with such studies: the structure must be stable and predictable. ose molecules can easily change their structures due to environmental changes such as the nature of the solution and the vacuum, and to intra-charge repulsion with many charges. 2,53,55,61) When the structure is unstable and unpredictable, it is not possible to correlate series of mobility peaks to those of charge numbers. e charge is speculated from the mobility obtained in IMS measurements.
To avoid the di culties associated with multiple charges, charge reduction has been utilized, especially in IMS studies. 24,25) Charge reduction is performed by means of a "neutralizer" with radioactive materials such as 241 Am where small positive and negative ions produced by the radiation become attached to sample ions with multiple charges through the attractive Coulomb force between them. Finally the number of the charge of the sample ions is reduced to 0 or ±1 as described to be "neutralizer" literally. e neutralizer is located between two IMS spectrometers in tandem IMS systems. e rst spectrometer selects ions with some mobility, which can have various sizes and charges. To determine the size, the charge is reduced to unity by the neutralizer followed by the second mobility spectrometer. In the second IMS, the size is determined from the xed unit charge.
In this case the problems associated with multiple charges are resolved but a new problem associated with the small charge appears. e sensitivity of the electron multiplier or other detectors for the ions with small charge is too low to permit their use in usual MS. So condensation-particlecounters (CPC) are used for the detection. To be detected with light scattering in CPC, charged particles are enlarged by nucleation with an alcohol such as n-butanol on the particles in supersaturated atmosphere. 65,66)

Charge detection Direct charge detection
Charge itself has not been typically observed in MS. e accelerated high-energy ions are introduced to an electron multiplier which produces millions of secondary electrons in the device to be detected as a pulse current. We can then count the numbers of ions through the pulse current but usually not the charge. Recent progress in electronic devices makes it possible to directly observe the charge of a single ion. 4,44) is technique is particularly useful, not only for determining mass from m/z but also for detecting heavy ions themselves where the sensitivity of the electron multiplier such as SEM and MCP is dramatically degraded because of small velocities even for highly accelerated ions. 13,14) Signi cant progress has been recently made on techniques for charge detection for being developed as charge detection mass spectrometry (CDMS), which was originally developed in 1960. 4 Charge sensitive ampli er (CSA) itself has a long history. Its main application is to resolve energy of radiation such as gamma rays with a semiconductive detector where the energy of the radiation is proportional to the number of electron-hole pairs or the induced charge. 14) ere are several commercial CSA such as A250 (AMPTEK) and SD-37 (Hamamatsu) with sensitivity as low as several hundreds e/mV as the ratio between the input charge and the output voltage. e sensitivity is not su cient to permit ordinary MS to detect ions with one or two e but is applicable to the detection of multiply charged heavy ions. 4,[40][41][42][43] Figure 7 shows a schematic diagram of CSA connected to the detector for heavy ions shown in Fig. 3. 41) As described in the "Ion Trap" section, the ions with the selected m/z by tuning the RF frequency are ejected from the trap and introduced to hit the detector which consists of a disk with a diameter of 1 cm as the Faraday plate. e ampli er detects the charge through the plate and outputs a voltage pulse with the height that is proportional to the charge. e pulse shape is shown in Fig. 4. 41) e mass and charge are simultaneously determined through m/z and z obtained from the peak position of the ejected timing and from the peak height, respectively. 41) CSA consists of a charge integrator, a low pass lter ampli er, a test pulse attenuator, and the Faraday plate represented as a white blue ellipse (Fig. 7), which corresponds to the plate in Fig. 3. 41) e charge integrator detects the charge and accumulates the image charge at the Faraday plate induced by ions to be detected. e low pass lter ampli es the signal and reduces high-frequency noise.
e test pulse attenuator functions to calibrate the charge sensitivity of CSA. e sensitivity is determined by the transmittance of Q1 and capacitance of the gate, C1, C2, and the Faraday plate, which are strongly dependent on parts to parts uctuation and the working temperature of the CSA. To calibrate the sensitivity for a precise ion charge evaluation, a xed voltage pulse is applied to the test pulse input. e test pulse attenuator is designed so as to inject the charge of 63,000 e to the Faraday plate with a test pulse of 1 V. e test pulse is attenuated by 1/101 with R4 and R5 resistor dividers and the charge is injected through C2 of 1 pF. When we apply a test pulse of 1 V, a voltage difference of 10 mV is applied across C2 where the charge of Q=C V=1 pF×10 mV=10 fC=63,000 e is accumulated. With the circuit and the calibration, the charge conversion of 1 mV/50 e and the noise of 10 mV (rms), corresponding to about 500 e rms, are obtained. 41) However it is very di cult to determine the exact sensitivity, even with this test circuit, due to the uctuation. e charge of an ion including its image charge is accumulated on the Faraday plate while the ion approaches the plate from the trap. e sequence of the charge accumulation and discharge is shown in Fig. 8. While a multiply charged positive ion approaches the conducting Faraday plate, the image charge (negative in the gure) to compensate the eld induced by the charge of the ion (positive in the gure) appears on the surface of the plate near the ion. A capacitor (C) and a registor (R) are connected to the plate from the ground. ose are the key parts of the integrator of the ampli er (Fig. 7). e capacitance of the capacitor shown in Fig. 8 is actually distributed to C1, C2 and a gate (terminal 1) of Q1 in the integrator and the test circuits. e register R corresponds to R6. Because the capacitance of those parts is much larger than that of the plate, the counter charge of the image charge is collected on the parts represented as capacitor C in Fig. 8. As the ion approaches the plate, the charge on C increases as well as the image charge.
e voltage on C increases until the ion hits the plate to neutralize the charge on the ion and the image charge. A er the collision, the charge and the voltage on C decrease gradually because of the discharge through the resistor of R. e voltage on the capacitor is sensed and ampli ed by Q1 of an N-ch junction eld e ect transistor (Nch-JFET) and U1B of a high-impedance low noise operational amplier in the integrator (Fig. 7) followed by the low pass lter ampli er for further ampli cation and noise reduction. e ampli cation is performed "inversely" so that the actual outputs for positive ions are negative-going peaks with a period of around 10 ms (Fig. 4). e ground level of C and R is not always 0 V but actually is controlled by the feedback of the operational ampli er of U1B to keep "virtual short" between "+" and "−" terminals of U1B, which results in the actual ampli cation. Figure 8, however, shows the basic circuit operation mechanism.
CSA has many characteristics such as charge sensitivity, a discharge time constant, and a noise level. Charge sensitivity is one the most important characteristics of charge detection, which is determined mainly by the Q1 and C1 values for the integrator. To enhance the sensitivity, the total capacitance C should be as low as possible, since the signal voltage is de ned as ∆V=q/C where q is the accumulated charge. For the detection of heavy ions from the trap, however, the capacitance C should not be too small because of the accumulation time constant τ determined by the product of the capacitance by resistance R of R6 as τ=C×R. 41) e accumulation time of the image charge is around ms due to the large plate size and slow ion velocity coming from the trap. 41) us the integrator must wait until the accumulation of the charge is complete, otherwise the accumulated charge would be lost. e long accumulation of 10 ms is achieved using large resistor of 10 GΩ of R6. With these customization for the heavy ions, the sensitivity of 50 e/mV and the noise level of 500 e are achieved. 41) e output voltage is basically proportional to the detected charge but the proportional factor or sensitivity always strongly depends on the devices on each ampli er and on the working temperature of the CSA. e calibration is also di cult because the production of the precise amount of charge is not so easy. Consequently the accuracy of the detected charge is not so high. e method achieves high-sensitivity for single particle mass spectrometry but the charge sensitivity and accuracy are not so high. Further development will be necessary.

Indirect charge detection
Direct charge detection is a powerful method. However indirect charge detection for measuring "image charge" also has a long history. e method has been widely used in trap type mass spectrometry such as Fourier transform ion cyclotron resonance mass spectrometry (FTICR) and Orbitrap ™ from ermo Co., Ltd. 68,69) Both of the trap type MS methods have achieved high-resolutions of up to 10 5 on m/z, which is very hard to be achieved by other methods. To achieve such a high resolution, Fourier transformation of ion movement in the trap is crucial. With a specially designed magnetic or electronic trap, the trapped high-energy ions continue long lasting periodical movements dictated by their m/z. e ultrahigh vacuum and the image charge detector realize the tracking of the movements. 68,69) From the Fourier transformation of the detected movements, whole ion species with di erent m/z values are identi ed as an intensity of each frequency component. is advantage contributes the throughput: all ions with di erent m/z can be analyzed from one track of the movements with Fourier transformation. To detect all species with good S/N, the frequency and the frequency distribution of the movements should be high, around MHz, requiring the use of a highfrequency broadband CSA to detect image charge because the resolution and sensitivity increase with increasing number of cycles of the periodical movements. 68,69) Based on those features, this indirect charge detection has been developed to enhance the detection sensitivity and the resolution of charge evaluation for a single heavy ion with multiple charges up to viruses as indirect CDMS recently. 5,59,70-72) Figure 9 shows a sequence of the indirect charge detection. 28,29,58,73) A tube like detector (the half of bottom is shown here) to which a capacitor (C I ) and an inverted charge sensitive ampli er (ICSA) are connected. e ICSA is similar to the circuit of Fig. 7, but the output of ICSA is connected to a sort of "di erentiating circuit" to detect the precise timing of the ion motion. 28,29) e di erentiator has many patterns of implementation but here is shown a simpli ed capacitor(C D )-registor(R D ) di erentiator. e inversion is mainly caused by Nch-JFET in Fig. 7 as the rst stage of the charge ampli er. e results of the indirect CDMS presented here and in the following sections are obtained by an A250 (Amptek) with Nch-JFET, which is di erent from the circuit in Fig. 7. ere are many circuit designs and implementations not to use the "inversion way." However all the results are consistent with the inversion way so that ICSA is adopted throughout in this review. e upper of the gure shows the ion motion while the bottom shows the input voltage of ∆V i as the voltage difference across C I and the nal output signal of V o corresponding to the processes described in the upper. e ion initially approaches the detector invoking an image charge (1). When the ion enters the tube detector perfectly, the image charge is accumulated and ∆V i reaches maxima (2). e connected ICSA ampli es the detector signal inversely with a sensitivity of around 10-1,000 e/mV. e amount of the image charge as well as ∆V i is constant until the ion is inside the detector tube (3). e output voltage of V o , on the other hand, decreases by the current through the registor R D to V o =0. When the ion begins to leave the detector (4), the image charge and ∆V i decrease resulting in an increase in V o until the ion nishes to leave with ∆V i as 0 and V o as the maxima (5). Finally both voltages go to zero (∆V i =V o =0) with the discharge (6). Here again, the ground level of C I is not always 0 V but is controlled by the feedback. e amplitude and the peak to peak time di erence are proportional to the charge and the time of ight (TOF) of the ion, respectively. e observed amplitude with the amplier sensitivity of −24 e/mV is around 80 mV for the ion of polyethylene oxides with the charge of +1,900 e. e TOF observed for the same ion is around 30 µs with the velocity of 1,400 m/s. 28) e charge is proportional to z so that the charge is deduced directly from the amplitude, providing there is no noise. 28) On the other hand, TOF depends not only on the velocity gain of the ions by the electrostatic acceleration but also on the initial velocity of the ions (v I ) induced by gas ow at an ESI source for example. Since the ions are so heavy, the e ect of the initial velocity is large. For example, we get 830 eV as kinetic energy in the case of m=1 MDa and v I =400 m/s. Finally m/z is obtained from TOF as where V is the acceleration voltage, L is the length of the detector tube. 28,74) Indirect CDMS measurement can be performed with this single-pass measurement. 28) Mass and charge information is deduced from the obtained z and m/z. However the charge information especially has large uncertainty because of the noise of the amplitude similar to the direct CDMS. To reduce the noise and the uncertainty of the charge information, averaging is the most e ective technique. at can be performed by using many electrodes up to 22 74) or placing the detector in an ion trap. 5,58) Figure 10 shows a schematic view of the multi-pass CDMS with the trap detector. e system consists of an ESI ion source, an ion guide, a TOF, an energy selector, and a trap detector. 75) Ions produced with the ESI source are introduced to the energy selector through the ion guide and the acceleration region of the TOF mass spectrometer for temporal evaluation. Energy selection is performed with a dual hemispherical de ection analyzer (HDA) because the m/z measurement signi cantly depends on the kinetic energy of the ions. e HDA consists of two concentric hemispherical electrodes with di erent potentials having radii of 19.05 and 31.75 mm for the inner and outer hemispheres, respectively. ree apertures with diameters of 2.54 mm are equipped in the entrance, middle, and exit parts of HDA. To achieve high energy selectivity, the reduction of angular deviation of the ion trajectory, and the deceleration and acceleration of ions across HDA, and the ion focusing are employed. With these techniques, the energy resolution of 0.45% with a spread of 99.75-100.20 eV is achieved. 75) A er the selection of ions with the kinetic energy of 100 eV/ charge, the ions enter the trap detector through the hole shown in the expansion of the gure. 5) e potentials of the endcaps of the trap are periodically manipulated to hold and eject the ions with a cycle time from tens of ms to several seconds. e trapped ions oscillate in a eld produced by shields and caps. In the oscillation, the ions enter and leave the center image charge detector with a tube-like structure, as shown in Fig. 9. With this motion the potential of the detector goes up and down through the charge accumulation and discharge processes as shown in Figs. 9 and 10. 73) us obtained detector signal is ampli ed (Fig. 9). To reduce noise, the Nch-JFET (Fig. 7) is cooled down cryogenically with liquid nitrogen and whole ampli er is located near the detector in the vacuum chamber. e temperature in a measurement is estimated to be 125 K. 71) e output signals are averaged to reduce the noise up to for several seconds or during several ten thousands of oscillations. e process from the thus obtained oscillations as time domain signals to a mass histogram is shown in Fig. 11. e time domain signals of each measured ion are analyzed in terms of the frequency and the amplitude. e m/z is obtained from the frequency while the charge of z is ob- tained from the amplitude. e data for both single ions are combined to determine the mass of m by multiplying m/z by z. Finally the mass histogram is constructed through the analyses on many ions. e m/z of ions is actually obtained from the fundamental frequency f of the oscillation and the selected energy E through the following equation 73) : 1.8 .
e dependence of f on E in Eq. (3) is not proportional to E , which would be expected from the grounded detector tube between steep potential walls similar to a particle in a box.
is approximately reciprocal energy dependence clearly shows that the ion spends most of the time in the caps, and not in the tube. 73) e charge z is obtained from the amplitude analysis based on Fourier transformation. For example, pyruvate kinase (PK) 16-mer ions of (PK 4 ) 4 with 72 e (m/z=13.5 k) and 100 eV/charge has the fundamental frequency f=13.9 kHz. 72) Figure 12 (le ) shows the obtained charge histogram of PK ions trapped for three seconds up to 60,000 oscillations where 3125 ions are collected. 72) e charge states are almost perfectly resolved with an uncertainty of less than 0.2 e. e superstructure with the peak at 33 e arises from its tetramer of PK 4 . e other peaks centered at 47, 59, and 72 are due to (PK 4 ) 2,3,4 , respectively. e mass histogram of the PK ions is constructed from the obtained information on the charge of z and the ratio of m/z by multiplying m/z by z (Fig. 12 (right)). 72) e inset of Fig. 12 (right) shows the expansion of (PK 4 ) 2 at 480 kDa. e blue and red lines show the mass peaks obtained with low (0.2 e) and high (0.65 e) charge uncertainty. 72,76) With strictly de ned charge information, the mass spectra obtained by this method has a very high resolution even in high m/z ratios of around 10,000 with 485 kDa and +47 e. In the usual TOF, the obtained mass spectra appear not as separated peaks but as overlapped ones. 23) Much heavier samples such as viruses are also observed by this CDMS in which the mass and the charge reach the level of 25 MDa and 600 e. 34) To achieve a high sensitivity and accuracy especially in terms of charge, this measurement system requires conditions of a single ion trapped, no energy loss, and a long trap lifetime, some of which may be realized by a no collision condition. 72) In terms of single ion condition, the usual trap type mass spectrometer deduces m/z by Fourier transformation with multiple ions trapped which cause dephasing or correlation in ion motions. In this case the lifetime is short resulting in a low S/N and accuracy. erefore, the proportionality between a signal amplitude and an intensity has been a serious problem. 68) To keep only single  ion trapped in CDMS, the potential of the endcaps is manipulated periodically depending on whether ions are in or not. 71,75) e number of trapped ions is deduced by analyzing the detected signal. When the number is zero or more than one, the data is discarded. e probability of the number of the ions obeys a Poisson distribution, which strongly depends on the ion intensity. To maximize the probability for the single ion condition, the ion intensity is monitored and controlled. It is di cult to realize a collision condition, even in an ultrahigh vacuum up to 3.6 −7 Pa by a di usion pump for preventing mechanical and electronical noise. 72) e mean free time is expected to around ms for a virus with a diameter of 16 nm under this pressure. 33,73) However the initial kinetic energy and mass are so large that collisions with light gas molecules such as nitrogen does not seem to disturb the oscillation in the trap. From the simple model of energy dissipation in thermal gas, the time constant for the energy loss would be predicted to be 3,000 s. 73) As the other path of the energy loss, the charging and discharging of the image charge ( Fig. 9) have no contribution. 71,73) e energy loss in the one cycle is estimated to be ∆E=(ze) 2 /C, where z is the charge number of the ion in the trap and C is the summed capacitance connected to the tube detector. Applying z of 100 and C of 10 pF, we get the energy loss of ∆E=2.6×10 −23 J=0.16 meV which can be neglected with the initial kinetic energy of 10 keV even in ten thousand cycles.
However some kinds of serious collisions clearly cause ion loss, 71) frequency shi s, 77) and charge loss. 73) e collisions are not serious in terms of the kinetic energy of the oscillating ions but they clearly limit the performance of CDMS. Investigations of the lifetime dependence on collisions revealed that multiple collisions such as three collisions for cytochrome c and four collisions for alcohol dehydrogenase are required to eject the ions from the trap. 71) e analyzed lifetimes and their molecular cross sections are in general agreement. e mechanisms for the requirement of multiple collisions are not fully understood but a trajectory shi in the trap caused by the collisions has been proposed for stability, which is described in the "Relationship between Charge and Mass or Size" sections. 77) e charge loss is also observed which may be caused by collisions. 73) Despite those di culties, long and many cycle oscillations up to three seconds and 60,000 times have been realized. 72) With this multi-pass image charge detection, the charge evaluation of a single ion has been measured with almost perfect accuracy. e potential shi of the detector by the image charge is estimated to be 1 nV so that the S/N is not su cient without an average. 73) Single-pass systems have also been reported. 28,74) However those systems tend to have a low sensitivity and low accuracy in terms of charge which is similar to the direct CDMS described above. Multi-detectors up to 22 are used to improve the S/N of the single-pass system 74) but the trap system shows much better performance. e noise is reduced as 1 N where N is number of average or number of cycle in this system. 58) Actually charge uncertainty is expressed as ∆z=83.33f −0.458 for 91 ms trap whereas m/z uncertainty is xed as ∆(m/z)/ m/z=0.008. 34) e m/z uncertainty is originated in mainly the energy spread of the energy selector and the trajectory spread in the trap. 71) With this sophisticated system, simultaneous measure-ments of mass and charge on very heavy ions can now be accomplished.

Other approaches
ere are several approaches for simultaneously detecting charge and mass. Here two examples are introduced. e rst one is kinetic energy detection by means of a superconducting detectors. 1,11,12,14,78) Ions accelerated under a potential di erence have the kinetic energy proportional to their charge. With this method, it is possible to distinguish N + and N 2 2+ . is method provides one of the most sensitive charge detectors. Actually, ions of multimers of polystyrene molecules with the mass up to MDa have been observed by this detector. 11) However, because of the low temperatures for superconductivity, it is very di cult to use them for general purposes. In terms of charge, the resolution is around 10. Energy resolution and linearity are not so high. However direct energy measurements could be expanded to detect their internal energy to distinguish whether the molecule is hot or cold. e other one is based on fabricated mechanical device technologies. 79,80) Nanomechanical resonators with the size of several hundreds of nm detect and measure the mass of tantalum clusters. 79) e clusters with a mass of from 1.3 to 3.4 MDa and charge from 1 to 3 e are produced by a sputtering gas aggregation, which are monitored by a TOF and a transmission electron microscopy. e clusters are deposited on the resonator, resulting in a slight shi in the resonant frequency from several tens of MHz by tens of kHz. e shi is su ciently large to detect and evaluate the mass of the clusters. In this study, the mass of the neutral clusters was determined to have almost the same mass as the charged ones. e high sensitivity for less than 500 kDa and the high resolution around 70 kDa are achieved. is method can detect neutral species which are still a challenging subject for MS. However the method can detect only a part of the clusters, about one particle out of a hundred million, due to the small cross section of the resonator. e sensor, in addition, may be used only at once because it would be di cult to remove the deposited particles from the sensor. ese problems can be overcome by integration of many devices and parallel operation of them. e charge of around 1,000 e on a toner particle, on the other hand, is also measured by these kinds of devices: a cantilever of atomic force microscopy through the detection of Coulomb image force between the particle and the cantilever. 80)

Relationship between charge and mass or size
One of the fundamental challenges in MS is to quantitatively elucidate the relationship between mass and charge. For industrial interests, the charged particles are treated in terms of particle manipulation such as toner for electrophotographic applications, electrostatic deposition, and electrostatic precipitator for prevention of dust explosion and for the preparation of clean rooms. 81,82) For fundamental research in MS, charge evaporation and the Coulombic explosion of highly charged large ions have been studied to reveal ionization processes of ESI. 2,21,83) In the early stage of ion production processes of ESI, the size of the charged particles produced at the capillary shrink due to solvent evaporation. In the process, the charge is constant until the size reaches a limit: the Rayleigh limit 84) and the ion emission limit. 26,27,83,85) e number of charge corresponding to the Rayleigh limit (n R ) and the ion emission limit (n IE ) depend on the diameter of spherical droplets (D) as where σ, E * , and ϵ 0 are the e ective surface tension of the droplet, the critical electric eld on the droplet surface emitting ions, and vacuum permittivity, respectively. As a function on the diameter D, n R ∝D 1.5 and n IE ∝D 2 . So in the larger size region n R dominate the charge whereas n IE in the smaller region. 24,27) ose limits have been investigated through simultaneous measurements of charge and size. In the larger size region of micro-droplets, ethylene glycol droplets produced by a piezoelectric injector with a radius of 50 µm in an ion trap are investigated via charge and size relationships by the light scattering for size evaluation and by levitation voltage scanning for charge and gravity evaluation. 26) During the trapping of several hundreds of seconds, particle size gradually shrinks but the charge is abruptly decreased by up to several tens of percent suggesting Coulomb explosion. e relatively large size make it possible to directly measure particle size by light scattering. When the particles are stabilized, the charge is much smaller than the limit. 35) A similar investigation was performed by direct and indirect CDMS on the charged polystyrene particles produced by ESI with various solution, 28,30) and by LIAD with corona discharge. 40,41) e maximum charge of polystyrene particles produced by ESI with water/methanol (50 : 50, v/v) depend on their mass within the Rayleigh limit R , q M = 0.06375 (6) where q R is the number of charge corresponding to the Rayleigh limit, and M is the mass of the particle in Da. 30) Here, the density of the particle and surface tension of the solution are assumed. 28,30) e CDMS observation reveals that the limit dependence holds on the particles with diameters from 78 to 143 nm where the average charge is 70-80% of the limit. 30) On the other hand, the maximum charge is much smaller in the case of LIAD (Fig. 3). e maximum charge is around 2.0×10 5 for a particle with a diameter of 15 µm and an estimated mass of 1.1×10 15 Da, which would be 2.1×10 6 in ESI from Eq. (6). In spite of the less maximum charge, the diameter dependence from 3 to 29.6 µm of polystyrene particles with LIAD shows that the average charge varies from 4,250 to 1.3×10 4 following the relationship between charge q AV and diameter D as , which is the same as the dependence of ESI (Eqs. (4) and (6)). e agreement suggests that similar processes restrict the maximum charge on particles in ESI and LIAD with corona discharge.
To investigate much smaller region, globular proteins are studied by ESI-MS assuming native structures. 83) e obtained charge states of the proteins are much smaller than those expected from the Rayleigh limit of Eq. (4) and the dependence of charge on the diameter of a protein is in good agreement with the ion emission model of Eq. (5) suggesting the existence of the ion emission processes.
From the data tting to Eq. (5), a few critical electric elds of E * and their dependence on the size are obtained, which also supports the ion emission processes. In spite of these successful results, the study again shows the limit of MS: assumed structures and restricted size controllability. We cannot use prede ned large particles with a large charge because we cannot identify the charge and the mass simultaneously only from m/z. e samples, then, are restricted to the smaller globular proteins with well know structures. e limit can be overcome with IMS measurements performed using the tandem system with neutralizer described in the "Ion Mobility Spectrometry" section. 24,27) Prede ned polystyrene, polyethylene glycol, sucrose, and metal particles with a diameter from 10 to 500 nm are ionized by ESI when suspended in water/methanol (50 : 50, v/v) and 1 mM ammonium acetate followed by a simultaneous charge and size measurement with the tandem IMS. Figure 13 shows the thus obtained plot of charge versus size. Clearly the size dependence changes at around 40 nm suggesting a change in criteria between the Rayleigh limit and the ion emission limit. In the larger region more than 40 nm, the charge dependence ts well to Eq. (4) and consequently to Eq. (6) with conversion from D to M .
ose results are consistent with the ESI processes alluded to above. However, the discussion on the obtained relationship between charge and size assumes perfectly spherical droplets which may not be realistic. 2) With structural deformation of the droplets, which could be caused by structural vibrations, collisions, or external electric elds, acute or high-eld positions like a vertex of a Taylor cone should be produced where the asymmetrical ssion or ion emission is preferred. 2) However it is very di cult to discern the details of the ESI processes, especially for rapid charge loss processes, because light scattering and IMS are "slow" measurements revealing only the stability of the nal products. Measurements on mass versus charge have been not been performed on the emitted ions with small mass and charge but, rather, on the nal ones with large masses and charges. High-speed observations both on the emitted Fig. 13. Relationship between charge and size of prede ned particles of polystyrene, polyethylene glycol, sucrose, and metals with the diameter from 10 to 500 nm, which are ionized by ESI with their suspension in 50% methanol, 50% water, and 1 mM ammonium acetate. 27 ions and the nal products have been di cult. 2,73) e indirect CDMS with the ion trap is suitable method on this subject. With an oscillation frequency of tens of kHz, the sensitivity of single ion detection, and the high resolution both on mass and charge, small ion emissions from virus ions with the charge of 146 e and the mass of 4 MDa are observed. 73) e emission is actually observed through the change of the oscillation frequency of 10 kHz with the shi around 50 Hz because the amplitude corresponding to the charge is less reliable due to the noise. Careful analyses have been performed on the processes involving collision with bu er gas, solvent evaporation, ion emission, and Coulomb interaction between ion and image charge. e frequency shi is caused by one charge emission with mass of 1,000 Da. Total mass loss is 20 kDa due to solvent evaporation in three seconds. Most of ions (43%) have at least one emission while a few of them (11%) have twice or more emissions in three seconds. e emission is promoted by the electric eld in the trap. CDMS cannot only characterize mass and charge of the heavy and highly charge ions but also track the change of them with high time resolution.

Structural analyses of large system
With the methods mentioned above, large systems such as cells, viruses and nano composites are within the scope of MS. e cellular uptake of nano/microparticles has been investigated by the direct CDMS with LIAD. 4) NTERA2 cells are incubated with gold nanoparticles with diameters of 30 and 250 nm. e observed mass of the cells increases with increasing incubation time. e mean mass increases 60% and 200% with the 30 nm and the 250 nm particles, respectively. 4) Figure 14 shows the incubation time dependence of the average numbers of uptaken (a) 50 nm gold particles by NTERA2 cells and (b) 100 nm polystyrene particles by Raw264.7 cells and the corresponding images of transmission electron microscopy (TEM). 4) e red circles and lines of Figs. 14a and 14b represent the particle numbers observed by direct CDMS while the black squares and lines of Fig. 14a represent those observed by ICP-MS. Both results are in good agreement with each other showing that direct CDMS is as reliable as ICP-MS in terms of the quantitative measurements. TEM measurements also supports the cellular uptake of the gold particles. However ICP-MS cannot be applied to polystyrene particles because the method is strongly dependent on key elements such as gold. In this case, TEM is used as a unique measurement method, which has less reliability as the quantitative measurements. CDMS, in turn, can detect the uptake of polystyrene particles by directly observing the mass of cells (Fig. 14b). Here the features of MS, such as material independence and quantitative measurements, are still valid in CDMS. Figure 15 shows mass spectra and a TEM image of virus capsids encapsulating scDNA. 86) A capsid is the protein shell of a virus assembled from the capsid viral protein (VP). e sample used here is recombinant adeno-associated viruses of serotype 8 (AAV8), which are promising vectors for human gene therapy. AAV is constructed from 60 copies of three di erent VPs (VP1, VP2, and VP3). VP1 is the longest with 738 residues and mass of 81,624 Da while VP2 and VP3 are shorter with mass of 66,649 and 59,762 Da. e mass spectrum (Fig. 15-1a) shows three peaks at 3.704±0.013, 4.4, and 5.095±0.025 MDa. e lightest one is empty AAV8, which is in good agreement with the expected mass of 3.729 MDa from the already known stoichiometry of V1 : V2 : V3 of around 1 : 1 : 10. e heaviest one is lled AAV8 with scDNA. e mass di erence between the lled and the empty ones is 1.392±0.013 MDa showing the expected sequence mass of the scDNA (1.389 MDa). e close agreement indicates that the scDNA is mainly packaged without counterions. e broad peak around 4.4 MDa is due to partially lled ones. e intensity ratio of each peak (empty:partial: lled) is 35 : 42 : 23 which is consistent with that obtained from the TEM image where uniform white lled spots and rings represent lled and empty ones, respectively (Fig. 15-1b). e charge versus mass scatter plot of the same sample clearly show that there is large charge distribution ( Fig.  15-2a). 86) Two charge states are found in the empty capsids, which are due to di erences in compaction. 87) e compact capsids without defects have a perfect icosahedral structure and have less chance to acquire a charge in ESI processes. 87) e empty capsids with some defects have a slightly larger charge. e lled ones, on the other hand, have much wider Similar structural studies on devastating pathogen viruses such as hepatitis B virus (HBV) have been performed. e building block for HBV capsid is core protein assembly domain Cp149 dimer. e capsid consists of 90 or 120 dimers with icosahedral structures. e icosahedral structures are observed by TEM with spherical shapes, but it is di cult to evaluate intermediate and structures with defects. With CDMS, the structures of intermediate are investigated. From the perfect icosahedral structure with 120 Cp149 dimers, 3 to 16 dimers are lost, thus creating a hole on the shell, which are also observed by TEM. 33) Figure 15-2b shows an m/z spectrum constructed from the charge vs. mass scatter plot by scanning diagonal lines in Fig. 15-2a. 86) Because the averaged charge is almost same, some information on three di erent species with di erent masses can be obtained as three major peaks in the m/z spectrum of Fig. 15-2b. However there are many minor peaks arising from widely distributed charge states and the relative abundances are totally di erent from those obtained from the mass spectrum. CDMS will play crucial roles in the quantitative abundance evaluation and defect evaluation, which are generally di cult for other methods. Figure 16 shows CDMS spectra of polystyrene(PS)/silica multipods and corresponding TEM images. 31) e particles have composite structures with center silica particles surrounded by PS particles. e composite structures of tetrapods (TP), hexapods (HP), and dodecapods (DDP) are mainly controlled by the size of center silica particles, which are shown in Figs. 16a, 16b, and 16c, respectively. Apparently each charge vs. mass scatter plot of Fig. 16 shows two components, corresponding to the free PS par-ticles and the composite particles. e mass of each component is 2, 10.4, 15.5, and 30.4 GDa, for free PS, TP, HP, and DDP, respectively. e relative proportions obtained by TEM and CDMS are in good agreement with each other. To elucidate relative proportion, mass information is more reliable than that of TEM because the number of detected ions are much larger than that of analyzed images, and because images are sometime di cult to be analyzed. It is possible to quantitatively analyze much larger numbers of samples with CDMS, which cannot be treated by the usual MS. Furthermore, the slopes in the spectra, charge versus mass, decrease from TP (Fig. 16a) to DDP (Fig. 16c) suggesting "accessible surface area" (ASA) of the composite nanoparticles. Since DDP has a compact structure compared to that of TP, the fact that charge/mass of DDP is smaller than that of TP can be explained by the di erence in ASA. e detailed structure of those relatively large system can be studied by CDMS.
Not only mass and charge but also cross sectional information can be obtained by CDMS, which can be used to directly explore structures of heavy molecules. 77) Cytochrome c, ubiquitin, and Bovine serum albumin (BSA) ions are produced by ESI with charge of +15, +10, and +50 e, respectively. ey are introduced in CDMS with the energy of 202.4 eV/charge at a pressure of 5×10 −9 Torr. In the trap of CDMS, ions collide with background gas, which leads to frequency shi s. From the amount and the intervals of the frequency shi s, the collision cross section can be evaluated. is trap type CDMS can track the changes of charge, mass, energy, and the cross section for long-term up to several seconds with high time resolution up to tens of µs. is feature should be emphasized. As described in the "Relationship between Charge and Mass or Size" sections, the frequency of the ion in indirect CDMS is sensitive to al- most every characteristic of the ion, including energy, mass, charge and so on. 73) In addition, the frequency dependence on those characteristics is determined by the design of the trap. For example, the frequency dependence in this study on the ion kinetic energy (E) is represented as 77) which is totally di erent from that of Prof. Jarrold's group represented by Eq. (3). 73) Careful analyses must be performed to elucidate the nature of the frequency shi and to deduce the information of ions. 73,77) CONCLUSION Recent topics on mass and charge measurements on heavy ions are introduced in terms of technical issues and ongoing results. e concepts and basic techniques have been developed for long time but recent progress makes it possible to simultaneously detect the mass and charge of single heavy ions. With this method, large systems such as cells and nano composites are within the scope of MS. Quantitative, statistical, and material independent evaluations will widely be used in various eld. However the need for many improvements is inevitable and the most urgent one is throughput.
As described above charge measurements must be performed on every single ions in CDMS regardless of the way of direct or indirect. To deduce statistically meaningful information, as many as ions, say, up to ten thousands should be observed. e situation is the same even in the case of conventional MS but the precise charge detection requires long measurement time resulting in low throughput. Low throughput is particularly serious in indirect CDMS. Because a single ion must be trapped for long time up to several seconds to achieve high charge sensitivity and accuracy, the throughput for the whole measurement is low with substantial time being required to permit information on many ions, i.e., up to ten thousand, to be accumulated. e number of ions and the frequency used in CDMS are one and tens of kHz, respectively, which are much smaller than those of FTICR or Orbitrap ™ .
Even with those di culties, there are many ways to improve performance. Conventional MS widely contributes to various elds with high sensitivity, throughput, and resolution but within the low mass region. CDMS is opening a new eld that cannot be accessed by conventional MS.
ere is no doubt that future devices will be equipped with commercial mass spectrometers and will be used to collect further information on complicated systems such as living organisms and real catalysts.