A combined ion source for fast switching between electrospray and matrix-assisted laser desorption/ionization in Fourier transform ion cyclotron resonance mass spectrometry

A new ion source has been developed for Fourier transform ion cyclotron resonance mass spectrometry (FTICRMS) that enables quick changes between matrix-assisted laser desorption/ionization (MALDI) and electrospray ionization (ESI) modes. When operating as an ESI source, the sample solution is sprayed through an angled nebulizer. The generated ions pass through a glass capillary followed by a skimmer and three sequential hexapole ion guides. Ions can be accumulated in the third hexapole (storage hexapole) before they are injected into the ICR trap. The second hexapole is mounted on a movable platform which also carries the MALDI sample plate. During the switch from ESI to MALDI, this platform moves the second hexapole out of the hexapole series and locates a MALDI sample plate with 384 sample positions into the area directly in front of the storage hexapole. The storage hexapole is in a medium pressure chamber (MPC) which has windows both for the incoming laser beam and for the observation optics, as well as a gas tube for pulsing collision gas into the chamber. During the MALDI operation the focused laser beam enters the MPC, passes between the hexapole rods and irradiates a MALDI sample on the target plate. The sample molecules are desorbed/ionized into the storage hexapole and simultaneously cooled by collisions with the pulsed gas. Ions desorbed from multiple laser shots can be accumulated in this hexapole before they are transferred to the ICR trap. With the combined ion source a computer-controlled switch between MALDI and ESI modes is possible in less than a minute, depending on the position of the MALDI target on the 384-spot plate. Immediate acquisition of mass spectra is possible after mode switching without the need for tuning or re-calibration.     

In-source H/D exchange and ion-molecule reactions using matrix assisted laser desorption/ionization Fourier transform ion cyclotron resonance mass spectrometry with pulsed collision and reaction gases

Controlled in-source ion-molecule reactions are performed for the first time in an external matrix assisted laser desorption ionization (MALDI) source of a Fourier transform ion cyclotron resonance mass spectrometer. The MALDI source with a hexapole ion guide that was originally designed to incorporate pulsed gas to collisionally cool ions (Baykut, G.; Jertz, R.; Witt, M. Rapid Commun. Mass Spectrom. 2000, 14, 1238-1247) has been modified to allow the study of in-source ion-molecule reactions. Upon laser desorption, a reaction gas was introduced through a second inlet and allowed to interact with the MALDI-generated ions trapped in the hexapole ion guide. Performing ion-molecule reactions in the high pressure range of the ion source prior to analysis in the ion cyclotron resonance (ICR) cell allows to maintain the ultra high vacuum in the cell which is crucial for high mass resolution measurements. In addition, due to the reaction gas pressure in the hexapole product ion formation is much faster than would be otherwise possible in the ICR cell. H/D exchange reactions with different peptides are investigated, as are proton-bound complex formations. A typical experimental sequence would be ion accumulation in the hexapole ion guide from multiple laser shots, addition of cooling gas during ion formation, addition of reaction gas, varied time delays for the ion-molecule reactions, and transmission of the product ions into the ICR cell for mass analysis. In this MALDI source H/D exchange reactions for different protonated peptides are investigated, as well as proton-bound complex formations with the reaction gas triethylamine. Amino acid sequence, structural flexibility and folding state of the peptides can be seen to play a part in the reactivity of such ions.     

Inline pneumatically assisted atmospheric pressure matrix‐assisted laser desorption/ionization ion trap mass spectrometry

Atmospheric pressure (AP) matrix‐assisted laser desorption/ionization (MALDI) is known to suffer from poor ion transfer efficiencies as compared to conventional vacuum MALDI (vMALDI). To mitigate these issues, a new AP‐MALDI ion source utilizing a coaxial gas flow was developed. Nitrogen, helium, and sulfur hexafluoride were tested for their abilities as ion carriers for a standard peptide and small drug molecules. Nitrogen showed the best ion transport efficiency, with sensitivity gains of up to 1900% and 20% for a peptide standard when the target plate voltage was either continuous or pulsed, respectively. The addition of carrier gas not only entrained the ions efficiently but also deflected background species and declustered analyte–matrix adducts, resulting in higher absolute analyte signal intensities and greater signal‐to‐noise (S/N) ratios. With the increased sensitivity of pneumatically assisted (PA) AP‐MALDI, the limits of detection of angiotensin I were 20 or 3 fmols for continuous or pulsed target plate voltage, respectively. For analyzing low‐mass analytes, it was found that very low gas flow rates (0.3–0.6 l min^?1) were preferable owing to increased fragmentation at higher gas flows. The analyte lability, type of gas, and nature of the extraction field between the target plate and mass spectrometer inlet were observed to be the most important factors affecting the performance of the in‐line PA‐AP‐MALDI ion source. Copyright © 2010 John Wiley & Sons, Ltd.     

A novel fourier transform ion cyclotron resonance mass spectrometer with improved ion trapping and detection capabilities

A novel Fourier transform ion cyclotron resonance (FT-ICR) mass spectrometer has been developed for improved biomolecule analysis. A flared metal capillary and an electrodynamic ion funnel were installed in the source region of the instrument for improved ion transmission. The transfer quadrupole is divided into 19 segments, with the capacity for independent control of DC voltage biases for each segment. Restrained ion population transfer (RIPT) is used to transfer ions from the ion accumulation region to the ICR cell. The RIPT ion guide reduces mass discrimination that occurs as a result of time-of-flight effects associated with gated trapping. Increasing the number of applied DC bias voltages from 8 to 18 increases the number of ions that are effectively trapped in the ICR cell. The RIPT ion guide with a novel voltage profile applied during ion transfer provides a 3- to 4-fold increase in the number of ions that are trapped in the ICR cell compared with gated trapping for the same ion accumulation time period. A novel ICR cell was incorporated in the instrument to reduce radial electric field variation for ions with different z-axis oscillation amplitudes. With the ICR cell, called trapping ring electrode cell (TREC), we can tailor the shape of the trapping electric fields to reduce dephasing of coherent cyclotron motion of an excited ion packet. With TREC, nearly an order of magnitude increase in sensitivity is observed. The performance of the instrument with the combination of RIPT, TREC, flared inlet, and ion funnel is presented.     

In-cell matrix-assisted laser desorption-ionization fourier transform ion cyclotron resonance mass spectrometry

A new internal matrix-assisted laser desorption-ionization (MALDI) Fourier transform ion cyclotron resonance-mass spectrometry (FTICR-MS) method is introduced. The target is directly positioned at one trapping electrode of a single cylindrical ion cyclotron resonance (ICR) cell and becomes a part of it. The ionization occurs inside the ICR cell in contrast to external or near-cell MALDI-FTICR-MS techniques. Very efficient trapping and mass resolving power better than unit resolution of singly charged peptides and proteins ions up to 2000 u is possible by using only basic FTICR-MS techniques. The sole application of a pulsed retarding potential increases the mass range to 6000 u. No collisional cooling and quadrupolar excitation was done. Sensitivities below 1 fmol, and ion storage times of more than 15 s are shown. High resolving powers of 16,000 and 56,000 are obtained on bovine insulin (5.7 ku) and gramicidin D (1.9 ku), respectively.     

A high-resolution scanning microprobe matrix-assisted laser desorption/ionization ion source for imaging analysis on an ion trap/Fourier transform ion cyclotron resonance mass spectrometer

A new scanning microprobe matrix-assisted laser desorption/ionization (SMALDI) ion source for high spatial resolution has been developed for linear ion trap and Fourier transform ion cyclotron resonance mass spectrometry (FT-ICR-MS). The source is fully compatible with commercial ion trap flanges (such as the LTQ series, Thermo Fisher Scientific). The source is designed for atmospheric pressure (AP) operation but is also suitable for mid-pressure operation. The AP mode is especially useful for investigating volatile compounds. The source can be interchanged with other ion sources within a minute when operated in the AP mode. Combining high-lateral resolution MALDI imaging with high mass resolution and high mass accuracy mass spectrometry, available in the FT-ICR mode, provides a new quality of analytical information, e.g. from biological samples. First results obtained with the new ion source demonstrate a maximum lateral resolution of 0.6 by 0.5 microm. Depending on the limit of detection of the chosen mass analyzer, however, the size of the focus had to be enlarged to a diameter of up to 8 microm in the FT-ICR mode, in order to create enough ions for detection. Mass spectra acquired for analytical imaging were obtained from single laser pulses per pixel in all the experiments. This mode allows us to investigate biological thin sections with desorption focus diameters in the micrometer range, known to cause complete evaporation of material under the laser focus with a very limited number of laser pulses. As a first example, peptide samples deposited in microstructures were investigated with the new setup. A high quality and validity of the acquired images were obtained in the ion trap mode due to the low limit of detection. High mass resolution and accuracy but poorer image quality were obtained in the ICR mode due to the lower detection sensitivity of the ICR detector.     

Laser-induced fluorescence of trapped gas-phase molecular ions generated by internal source matrix-assisted laser desorption/ionization in a Fourier transform ion cyclotron resonance mass spectrometer

The combination of laser-induced fluorescence with mass spectrometry opens up new possibilities both for detection purposes and for structural studies of trapped biomolecular ions in the gas phase. However, this approach is experimentally very challenging, and only a handful of studies have been reported so far. In this contribution, a novel scheme for laser-induced fluorescence measurements of ions trapped inside a Fourier transform ion cyclotron resonance (FT-ICR) mass spectrometer will be introduced. It is based on an open FT-ICR cell design, continuous wave axial excitation of the fluorescence, orthogonal photon collection by fiber optics, and single photon counting detection. Rhodamine 6G ions generated by an internal matrix-assisted laser desorption/ionization source were used to develop and test the set-up. Due to photobleaching processes, the excitation laser power and the observation time window have to be carefully optimized. An ion tomography method was used to align the excitation laser. Potential applications for studying the gas-phase structure of fluorescent biomolecular ions and for investigating fluorescence resonance energy transfer of donor-acceptor pairs will be presented.     

Optimization of a quadrupole ion storage trap as a source for time‐of‐flight mass spectrometry

Designs of a quadrupole ion trap (QIT) as a source for time‐of‐flight (TOF) mass spectrometry are evaluated for mass resolution, ion trapping, and laser activation of trapped ions. Comparisons are made with the standard hyperbolic electrode ion trap geometry for TOF mass analysis in both linear and reflectron modes. A parallel‐plate design for the QIT is found to give significantly improved TOF mass spectrometer performance. Effects of ion temperature, trapped ion cloud size, mass, and extraction field on mass resolution are investigated in detail by simulation of the TOF peak profiles. Mass resolution (m/Δm) values of several thousand are predicted even at room temperature with moderate extraction fields for the optimized design. The optimized design also allows larger radial ion collection size compared with the hyperbolic ion trap, without compromising the mass resolution. The proposed design of the QIT also improves the ion–laser interaction volume and photon collection efficiency for fluorescence measurements on trapped ions. Copyright © 2011 John Wiley & Sons, Ltd.     

Deceleration of high-energy matrix-assisted laser desorption/ionization ions in an open cell for Fourier transform ion cyclotron resonance mass spectrometry.

A new method of ion deceleration in a Fourier transform ion cyclotron resonance (FTICR) open cell is described that improves the performance of FTICR-MS instruments equipped with an internal source for laser desorption/ionization. Ion deceleration occurs in the front trapping cylinder of an open cylindrical cell. Decelerating voltages up to 100 V can be applied for 10-500 micros to the front cylinder during ion introduction. The deceleration field is uniformly distributed along the cylinder length giving a "smooth" deceleration, which means that the deceleration is effective over a large time interval and a large m/z range. This results in improved trapping efficiency of high-energy ions. We demonstrate efficient trapping of high (m/z 66 kDa) mass ions and the possibility to reduce the width of the kinetic energy distribution of MALDI ions with this arrangement.     

A new hybrid electrospray Fourier transform mass spectrometer: design and performance characteristics

A new hybrid electrospray quadrupole Fourier transform mass spectrometry (FTMS) instrument design is shown and characterized. This instrument involves coupling an electrospray source and mass-resolving quadrupole, ion accumulation, and collision cell linear ion trap system developed by MDS Sciex with a home-built ion guide and ion cyclotron resonance (ICR) cell. The iterative progression of this design is shown. The final design involves a set of hexapole ion guides to transfer the ions from the accumulation/collision trap through the magnetic field gradient and into the cell. These hexapole ion guides are separated by a thin gate valve and two conduction limits to maintain the required <10(-9) mbar vacuum for FTICR. Low-attomole detection limits for a pure peptide are shown, 220 000 resolving power in broadband mode and 820 000 resolving power in narrow-band mode are demonstrated, and mass accuracy in the <2 ppm range is routinely available provided the signal is abundant, cleanly resolved, and internally calibrated. This instrument design provides high experimental flexibility, allowing Q2 CAD, SORI-CAD, IRMPD, and ECD experiments with selected ion accumulation as well as experiments such as nozzle skimmer dissociation. Initial top-down mass spectrometry experiments on a protein is shown using ECD.     

Electron transfer dissociation in the hexapole collision cell of a hybrid quadrupole-hexapole Fourier transform ion cyclotron resonance mass spectrometer

Electron transfer dissociation (ETD) of proteins is demonstrated in a hybrid quadrupole-hexapole Fourier transform ion cyclotron resonance mass spectrometer (Qh-FTICRMS). Analyte ions are selected in the mass analyzing quadrupole, accumulated in the hexapole linear ion trap, reacted with fluoranthene reagent anions, and then analyzed via an FTICR mass analyzer. The hexapole trap allows for a broad fragment ion mass range and a high ion storage capacity. Using a 3 T FTICRMS, resolutions of 60 000 were achieved with mass accuracies averaging below 1.4 ppm. The high resolution, high mass accuracy ETD spectra provided by FTICR obviates the need for proton transfer reaction (PTR) charge state reduction of ETD product ions when analyzing proteins or large peptides. This is demonstrated with the ETD of ubiquitin and apomyoglobin yielding sequence coverages of 37 and 20%, respectively. We believe this represents the first reported successful combination of ETD and a FTICRMS.     

A gated-beam electrospray ionization source with an external ion reservoir. A new tool for the characterization of biomolecules using electrospray ionization mass spectrometry.

In this work we describe a micro-electrospray ionization source equipped with an atmospheric pressure external ion shutter. The solenoid-activated shutter prevents the electrospray plume from entering the inlet capillary unless triggered to the 'open' position. When in the 'closed' position, a stable electrospray plume is maintained between the electrospray ionization (ESI) emitter and the electrically isolated face of the shutter. When the shutter is triggered, a 'slice' of ions is allowed to enter the inlet capillary and is subsequently accumulated in an external ion reservoir comprised of a radio frequency only (rf-only) hexapole and a pair of electrostatic elements. Following ion accumulation in the external ion reservoir, intact molecular ions of proteins, oligonucleotides, and noncovalent complexes can be stored for extended intervals (>30 minutes) prior to being transferred to the Fourier transform ion cyclotron resonance (FTICR) trapped ion cell for mass analysis. By introducing reactive gases directly into the external ion reservoir during the storage interval, ion-molecule reactions, such as H/D exchange, can be performed at high effective pressures. This scheme obviates the need for the long reaction times and delays associated with restoring base pressure in the trapped ion cell and allows H/D exchange reactions to be conducted in a fraction of the time required using conventional in-cell exchange approaches. The back face of the shutter arm contains an elastomeric material which can be positioned to seal the inlet to the mass spectrometer resulting in lower base pressure in the ion reservoir and the FTICR cell. Additionally, it is noted that blocking the ESI plume during non-accumulation events results in reduced fouling of the source electrodes and longer times between required source cleaning.     

Signal suppression in electrospray ionization Fourier transform mass spectrometry of multi-component samples

The high resolution, mass range and sensitivity of Fourier transform mass spectrometry (FTMS) suggest that it could be a valuable tool for the quantitative analysis of biomolecules. To determine the applicability of electrospray ionization combined with FTMS to the quantitation of biomolecules in multi-component samples, mixtures of varying compositions and concentrations of cytochrome c, angiotensin II, insulin and chicken egg white lysozyme were examined. The instrument used has an electrospray source with a hexapole trap to accumulate ions for injection into an ion cyclotron resonance mass analyzer. Linear responses for single component samples of angiotensin II and insulin were in the range 0.031-3 microM and those of both cytochrome c and lysozyme were between 0.031 and 1 microM. In examining various mixtures of the proteins with angiotensin II, it was found that the presence of the large molecules suppresses the signal of the smaller molecules. This is suggested to be a result of ion-ion interactions producing selective ion loss from either the hexapole trap or the ion cyclotron resonance mass analyzer trap. More massive, more highly charged ions can collisionally transfer large amounts of translational energy to smaller, less highly charged ions, ejecting the smaller ions from the trap. Mass discrimination effects resulting from the trapping voltage were also examined. It was found that relative signal intensities of ions of different masses depend on trapping voltage for externally produced ions. The effect is most significant for spectra including masses that differ by 30% or more. This suggests that for quantitation all samples and standards be run at a constant trapping potential.     

Calibration laws based on multiple linear regression applied to matrix-assisted laser desorption/ionization Fourier transform ion cyclotron resonance mass spectrometry

Operation of any mass spectrometer requires implementation of mass calibration laws to translate experimentally measured physical quantities into a m/z range. While internal calibration in Fourier transform ion cyclotron resonance mass spectrometry (FT-ICR-MS) offers several attractive features, including exposure of calibrant and analyte ions to identical experimental conditions (e.g. space charge), external calibration affords simpler pulse sequences and higher throughput. The automatic gain control method used in hybrid linear trap quadrupole (LTQ) FT-ICR-MS to consistently obtain the same ion population is not readily amenable to matrix-assisted laser desorption/ionization (MALDI) FT-ICR-MS, due to the heterogeneous nature and poor spot-to-spot reproducibility of MALDI. This can be compensated for by taking external calibration laws into account that consider magnetic and electric fields, as well as relative and total ion abundances. Herein, an evaluation of external mass calibration laws applied to MALDI-FT-ICR-MS is performed to achieve higher mass measurement accuracy (MMA).     

Ion trajectories in an electrostatic ion guide for external ion source fourier transform ion cyclotron resonance mass spectrometry

An electrostatic ion guide (EIG) that consists of concentric cylinder and central wire electrodes can transport ions efficiently from an external ion source to an ion cyclotron resonance (ICR) ion trap for mass analysis, with several advantages over current injection methods. Because the electrostatic force of the EIG captures ions in a stable orbit about the wire electrode, ions with initially divergent trajectories may be redirected toward the ICR ion trap for improved ion transmission efficiency. SIMION trajectory calculations (ion kinetic energy, 1–200 eV; elevation angle, 0.30 °; azimuthal angle, 0.360°) predict that ions of m/z 1000 may be transmitted through a strong (0.01 → 3.0-T) magnetic field gradient. Judicious choice of ion source position and EIG potential minimizes the spread in ion axial kinetic energy at the ICR ion trap. Advantages of the EIG include large acceptance angle, even for ions that have large initial kinetic energy and large radial displacement with respect to the central z-axis, low ion extraction voltage (5–20 V), and efficient trapping because ions need not be accelerated to high velocity to pass through the magnetic field gradient.     

A high pressure matrix-assisted laser desorption/ionization Fourier transform mass spectrometry ion source for thermal stabilization of labile biomolecules

A high pressure matrix-assisted laser desorption/ionization (MALDI) Fourier transform mass spectrometry (FTMS) ion source was designed and tested. With this design, pressure is pulsed to an estimated 1-10 mbar in the region of the MALDI sample during desorption with the result of significantly decreased fragmentation compared to similar systems operating with pressures of <0.1 mbar. The thermal stabilization of vibrationally excited ions under these conditions is shown with small peptides desorbed from the "hot" matrix alpha-cyano-4-hydroxycinnamic acid, and with the highly labile oxidized beta-chain of insulin. Fragile gangliosides with several sialic acid residues are desorbed under high pressure and remain intact without the typical losses of sialic acid, and a protein standard, ubiquitin (8565.64 Da), is desorbed with minimal dehydration. Under high pressure collisional cooling conditions, non-covalent matrix adduction to the molecular ions becomes prominent, but with the trapped ions in an FT mass spectrometer, the ions can be mildly activated to detach the matrix adducts. The new source, additionally, generates significant levels of the multiply charged ions which are commonly seen in MALDI-TOFMS, but are rarely observed in MALDI-FTMS. This effect is more likely due to the elimination of a mass filtering effect in the previous FTMS ion source than to collisional cooling of the ions.     

A new technique for unbiased external ion accumulation in a quadrupole two-dimensional ion trap for electrospray ionization Fourier transform ion cyclotron resonance mass spectrometry.

External ion accumulation in a two-dimensional (2D) multipole trap has been shown to increase the sensitivity, dynamic range and duty cycle of a Fourier transform ion cyclotron resonance (FTICR) mass spectrometer. However, it is important that trapped ions be detected without significant bias at longer accumulation times in the external 2D multipole trap. With increasing ion accumulation time pronounced m/z discrimination was observed when trapping ions in an accumulation quadrupole. In this work we show that superimposing lower rf-amplitude dipolar excitation over the main rf-field in the accumulation quadrupole results in disruption of the m/z discrimination and can potentially be used to achieve unbiased external ion accumulation with FTICR.     

Enhanced gas-phase hydrogen-deuterium exchange of oligonucleotide and protein ions stored in an external multipole ion reservoir

Rapid gas-phase hydrogen-deuterium (H-D) exchange from D(2)O and ND(3) into oligonucleotide and protein ions was achieved during storage in a hexapole ion reservoir. Deuterated gas is introduced through a capillary line that discharges directly into the low-pressure region of the reservoir. Following exchange, the degree of H-D exchange is determined using Fourier transform ion cyclotron resonance mass spectrometry. Gas-phase H-D exchange experiments can be conducted more than 100 times faster than observed using conventional in-cell exchange protocols that require lower gas pressures and additional pump-down periods. The short experimental times facilitate the quantitation of the number of labile hydrogens for less reactive proteins and structured oligonucleotides. For ubiquitin, we observe approximately 65 H-D exchanges after 20 s. Exchange rates of > 250 hydrogens s(-1) are observed for oligonucleotide ions when D(2)O or ND(3) is admitted directly into the external ion reservoir owing to the high local pressure in the hexapole. Partially deuterated oligonucleotide ions have been fragmented in the reservoir using infrared multiphoton dissociation (IRMPD). The resulting fragment ions show that exchange predominates at charged sites on the 5'- and 3'-ends of the oligonucleotide, whereas exchange is slower in the core. This hardware configuration is independent of the mass detector and should be compatible with other mass spectrometric platforms including quadrupole ion trap and time-of-flight mass spectrometers.     

Electrospray ionization—Fourier transform ion cyclotron resonance mass spectrometry at 11.5 tesla: Instrument design and initial results

Initial results obtained using a new electrospray ionization (ESI) Fourier transform ion cyclotron resonance (FTICR) mass spectrometer operated at a magnetic field 11.5 tesla are presented. The new instrument utilized an electrostatic ion guide between the ESI source and FTICR trap that provided up to 5% overall transmission efficiency for light ions and up to 30% efficiency for heavier biomolecules. The higher magnetic field in combination with an enlarged FTICR ion trap made it possible to substantially improve resolving power and operate in a more robust fashion for large biopolymers compared to lower field instruments. Mass resolution up to 10⁶ has been achieved for intermediate size biopolymers such as bovine ubiquitin (8.6 kDa) and bovine cytochrome c (12.4 kDa) without the use of frequency drift correction methods. A mass resolution of 370,000 has been demonstrated for isotopically resolved molecular ions of bovine serum albumin (66.5 kDa). Comparative measurements were made with the same spectrometer using a lower field 3.5-tesla magnet allowing the performance gains to be more readily quantified. Further improvements in pumping capacity of the vacuum system and efficiency of ion transmission from the source are expected to lead to further substantial sensitivity gains.     

Ideal velocity focusing in a reflectron time-of-flight mass spectrometer

A single-stage ion mirror in a time-of-flight (TOF) mass spectrometer (MS) can perform first order velocity focusing of ions initially located at a start focal plane while second order velocity focusing can be achieved using a double-stage reflectron. The situation is quite different when an ion source extraction field is taken into account. In this case which is common in any practical matrix-assisted laser desorption/ionization (MALDI) TOF-MS a single-stage reflectron, for example, cannot perform velocity focusing at all. In this paper an exact, analytic solution for an electric field inside a one-dimensional reflectron has been found to achieve universal temporal focusing of ions having an initial velocity distribution. The general solution is valid for arbitrary electric field distributions in the upstream (from the ion source to the reflectron) and downstream (from the reflectron to an ion detector) regions and in a decelerating part of the reflectron of a reflectron TOF mass spectrometer. The results obtained are especially useful for designing MALDI reflectron TOF mass spectrometers in which the initial velocity distribution of MALDI ions is the major limiting factor for achieving high mass resolution. Using analytical expressions obtained for an arbitrary case, convenient working formulas are derived for the case of a reflectron TOF-MS with a dual-stage extraction ion source. The special case of a MALDI reflectron TOF-MS with an ion source having a low acceleration voltage (or large extraction region) is considered. The formulas derived correct the effect of the acceleration regions in a MALDI ion source and after the reflectron before detecting ions.