Collisional Cross-Sections with T-Wave Ion Mobility Spectrometry without Experimental Calibration
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A method for relating traveling-wave ion mobility spectrometry (TWIMS) drift times with collisional cross-sections using computational simulations is presented. This method is developed using SIMION modeling of the TWIMS potential wave and equations that describe the velocity of ions in gases induced by electric fields. The accuracy of this method is assessed by comparing the collisional cross-sections of 70 different reference ions obtained using this method with those obtained from static drift tube ion mobility measurements. The cross-sections obtained here with low wave velocities are very similar to those obtained using static drift (average difference = 0.3%) for ions formed from both denaturing and buffered aqueous solutions. In contrast, the cross-sections obtained with high wave velocities are significantly greater, especially for ions formed from buffered aqueous solutions. These higher cross-sections at high wave velocities may result from high-order factors not accounted for in the model presented here or from the protein ions unfolding during TWIMS. Results from this study demonstrate that collisional cross-sections can be obtained from single TWIMS drift time measurements, but that low wave velocities and gentle instrument conditions should be used in order to minimize any uncertainties resulting from high-order effects not accounted for in the present model and from any protein unfolding that might occur. Thus, the method presented here eliminates the need to calibrate TWIMS drift times with collisional cross-sections measured using other ion mobility devices.
KeywordsTraveling wave Ion mobility Mass spectrometry Collisional cross-sections
Ion mobility spectrometry (IMS) separates gaseous ions on the basis of their collisional cross-sections, which depend on ion shape, mass, charge state, temperature, and ion-neutral interactions . IMS has been used in many applications, including the separation of atomic ions [2, 3], small clusters [3, 4, 5], tryptic digests [6, 7, 8, 9], and investigating the gas-phase conformations of biopolymers [10, 11, 12, 13], biopolymer complexes [14, 15, 16], and viruses . IMS can be done using static drift tube [18, 19, 20], field-asymmetric [20, 21, 22, 23], aspiration [24, 25], and traveling-wave [26, 27] IMS devices. In traveling-wave IMS (TWIMS), a potential wave is generated by applying a DC potential to a set of adjacent ring electrodes, and this wave is moved through the device with time . Some ions traverse the device at the velocity of the wave, and others are overtaken by the wave, resulting in ion separation [28, 29]. The shape of the wave and the distance between consecutive waves can differ between TWIMS devices depending on instrument design and parameters .
In static drift tube (DT)IMS, ion cross-section can be directly determined from the measured ion drift times when all experimental parameters are accurately known or by calibrating with ions with known collisional cross-sections [30, 31, 32]. Determining ion cross-sections with TWIMS is typically done by calibrating the drift times to collisional cross-sections measured using DTIMS [33, 34, 35, 36]. Cross-sections obtained for ions generated from denaturing solutions using TWIMS chemical calibration techniques are generally very similar to those obtained using DTIMS (average difference = 1%) [34, 37, 38, 39], although differences in cross-sections as high as 9% have been reported . Obtaining accurate collisional cross-sections for ions generated from buffered aqueous solutions in which the proteins have native conformations and activities using TWIMS is often more challenging [38, 40]. This is because the drift times of protein ions formed from buffered aqueous solutions in which proteins are folded increase more rapidly with increasing wave velocity than do the drift times of ions formed from solutions in which proteins are denatured. This difference in behavior has been attributed to collisional heating and subsequent unfolding of initially folded protein ions during TWIMS  and also to unspecified characteristics of the TWIMS separation mechanism . Methods for obtaining collisional cross-sections of ions formed from buffered aqueous solutions have been presented and rely on selecting calibrant ions that have similar rates of change in drift time with TWIMS wave velocity as the ions of interest [38, 40].
A method for directly measuring the mobility of ions using TWIMS was reported . SIMION modeling was used to derive an equation that relates the ion mobility and the wave velocity to the minimum wave height required to cause an ion to traverse the TWIMS device at the velocity of the wave. The minimum wave height is determined by incrementally increasing the wave height until the ion traverses the device at the wave velocity. Cross-sections obtained using this method are the same within 5% as those obtained with DTIMS . However, even though the motion of ions in TWIMS devices has been modeled [43, 44], there are currently no methods that enable cross-sections to be determined from a single TWIMS drift time measurement without prior calibration [14, 29, 36, 45].
Here, a method for relating TWIMS drift times with collisional cross-sections using computational simulations is presented. This method is developed using SIMION modeling of the TWIMS potential wave and equations that describe the velocity of ions in gases under the influence of electric fields. Cross-sections obtained using this method under conditions of low wave velocities are very similar to those obtained with DTIMS (average difference = 0.3%) for ions formed from both denaturing and buffered aqueous solutions. At high wave velocities, the collisional cross-sections obtained using the computational method presented here are significantly larger (as much as 32% larger) than those obtained with DTIMS, especially for ions formed from buffered aqueous solutions. These higher cross-sections may result from high-order effects not accounted for in the simple model presented here, although some protein unfolding during TWIMS as a result of collisional ion heating [41, 46, 47, 48] may also contribute. Results from this study show that ion collisional cross-sections can be determined from single TWIMS drift time measurements but that low wave velocities and gentle instrument settings should be used to reduce any uncertainties resulting from high-order effects not accounted for in this model and from any protein unfolding that might occur during the measurement.
Experiments are performed using a Synapt G2 high definition mass spectrometer (Waters Corp., Milford, MA, USA). Ions are formed by nanoESI using borosilicate capillaries with tips pulled using a model P-87 Flaming/Brown micropipette puller (Sutter Instruments Co., Novato, CA, USA). A platinum wire is brought into contact with the sample solution inside the capillary, and nanoESI is initiated by applying a ~800 V potential to the platinum wire relative to the potential of the entrance of the mass spectrometer. Flow rates in the helium and TWIMS cells are kept constant at 180 and 90 mL/min, respectively. The pressure in the TWIMS cell is measured using a model APG-L active Pirani gauge (Edwards, Crawley, UK) that is located within the TWIMS chamber, and this value was 3.2 mbar in all experiments. The measured drift times are adjusted by subtracting the time required for the ions to traverse the transfer TWIMS cell, which is located immediately after the TWIMS cell and immediately prior to the mass analyzer. This time is ~142 μs and is determined by dividing the 10 cm length of the transfer cell by the 703 m/s wave velocity used in the transfer cell, as described previously . With some wave conditions, low mobility ions do not traverse the TWIMS cell within the time frame of a single drift experiment. When this occurs, the measured drift times are adjusted by adding the 36.268 ms length of a single drift experiment. Two hundred drift bins are used for all experiments, resulting in a bin width of ~181 μs. SIMION ver. 8.0  is used to model the electric field along the axis of the TWIMS device using a pixel size of 0.10 mm. This pixel size was selected by incrementally decreasing the pixel size until the electric field strength no longer significantly changed with pixel size. The electric field strength changes by less than 1% at all points along the axis of the device as the pixel size decreases from 0.20 to 0.05 mm.
Bovine serum albumin, ubiquitin, equine cytochrome c, myoglobin, concanavalin A from Canavalia ensiformis, bradykinin, angiotensin II, and DL-polyalanine were obtained from Sigma-Aldrich (St. Louis, MO, USA), and acetonitrile, glacial acetic acid, and methanol were from Fisher Scientific (Fair Lawn, NJ, USA). Solutions were prepared in 18.2 MΩ water from a Milli-Q water purification system (Millipore, Billerica, MA, USA). Polyalanine solutions were prepared with 0.1 mg/mL analyte concentrations, and all other solutions were prepared with 10 μM analyte concentrations. Serum albumin and concanavalin A ions are formed from 200 mM aqueous ammonium acetate solutions in which they have native-like conformations and activities. Denatured polyalanine ions are formed from a 49/49/2 water, acetonitrile, acetic acid solution, and all other denatured protein and peptide ions are formed from 49/49/2 water, methanol, acetic acid solutions. DTIMS cross-sections for polyalanine were from reference , and all other DTIMS cross-sections were from reference . All DTIMS cross-sections were measured in nitrogen gas [39, 40].
Modelling the TWIMS Electric Potential
Calculating Ion Drift Times
The total distance an ion travels when multiple waves pass through the device is obtained by summing the distance the ion travels during each wave step. The initial ion position in the first computational wave step is arbitrarily set to 1 mm, but starting the ion at different positions on the wave results in the same transit time to within 1%. The final ion position in this wave step is computed from the initial ion position and the instrument dwell time. The potential wave is then stepped forward, resulting in a change in the electric field strength experienced by the ion. The distance the ion travels during this new wave step is then computed as a function of the initial ion position in this wave step and the instrument dwell time. The potential wave is stepped forward and the distance the ion travels during each step is computed over multiple wave steps until the motion of the ion through the device is well characterized.
In order to simulate this same ion under conditions where it is overtaken by the traveling waves, a 2000 m/s wave velocity and a 20 V wave height are used (Figure 2b). The results in Figure 2b are obtained with Equation 8 (black dashed line) and Equation 9 (blue line). When the ion is on the front of the wave, it moves forward through the device towards the mass analyzer, but when it is overtaken by a wave, it moves backwards through the device away from the mass analyzer (Figure 2b). Thus, the position of the ion inside the TWIMS device oscillates as waves are stepped through the device. The results in Figure 2b obtained with both Equations 8 and 9 indicate that under the conditions used here, the ion is overtaken by the wave once every four wave steps but on average moves forward through the device towards the detector, consistent with the motion of a low mobility ion moving through the device. Other models of the motion of ions in TWIMS devices have also shown ions traversing the TWIMS cell at the wave velocity with low wave velocities and the same ions experiencing numerous rollover events with high wave velocities .
Results and Discussion
Accuracy of the Computed Drift Times
The difference between the drift times that are measured in TWIMS and the calculated drift times modeled using the same experimental parameters used in the TWIMS measurements and the DTIMS cross-sectional values is small for ions formed from denaturing solutions (average difference = 2%) for wave velocities of ≤1500 m/s and both wave heights. These results indicate that TWIMS drift times for a wide variety of protein and peptide ions formed from denaturing solutions can be accurately predicted using the computational method presented here for low wave velocities. In contrast, the measured drift times acquired with a 2000 m/s wave velocity are significantly larger than the calculated drift times at this same wave velocity (average difference = 12% and 20% larger in Figure 4a and b, respectively). The difference between the measured and calculated drift times for ions generated from buffered aqueous solutions is also low for low wave velocities (average difference = 1% for wave velocities of ≤500 m/s), but the measured drift times are on average 16% and 25% larger than the calculated drift times for wave velocities of 1000 and 1500 m/s, respectively. The width of the ion mobility peaks increases as the wave velocity increases, and with the 2000 m/s wave velocity, the width of the peaks corresponding to the ions formed from buffered aqueous solutions are too broad to obtain measured drift times.
Obtaining Collisional Cross-Sections with the Computational Method
The TWIMS computational calibration cross-sections obtained for the ions formed from denaturing solutions are extremely similar to those obtained with DTIMS (average difference = 0.1%) for wave velocities of ≤1500 m/s. This uncertainty is similar to the uncertainty resulting from the standard experimental calibration approach  for obtaining collisional cross-sections with TWIMS (1% [34, 37, 38, 39]). These results indicate that the cross-sections for ions formed from denaturing solutions obtained using TWIMS computational calibration with low wave velocities are approximately as accurate as those obtained using TWIMS chemical calibration.
The collisional cross-sections obtained here with low wave velocities (≤500 m/s) for ions formed from buffered aqueous solutions are also very similar to those obtained with DTIMS (average difference = 1%, Figure 5, upper panels), but with 1000 and 1500 m/s wave velocities, the cross-sections obtained here are on average 16% and 25% larger, respectively, than those obtained with DTIMS. In striking contrast, the average difference is only 1% for the ions formed from denaturing solutions at these two higher wave velocities. The higher cross-sections obtained for the ions formed from the buffered aqueous solutions in which folded structures are adopted are consistent with these ions unfolding during TWIMS [41, 48].
The difference in the relationship between wave velocity and drift time for folded and unfolded protein ions has been reported previously [38, 41, 47, 48]. This effect has been attributed to conformation effects  and other unspecified factors, which result in longer drift times for folded protein ions than for unfolded protein ions . Ion heating inside TWIMS devices has been investigated previously by measuring the extent to which ions with known Arrhenius parameters (benzylpyridinium ions, protonated leucine enkephalin dimer, and holo-myoglobin) dissociate during TWIMS separation [46, 47, 48]. In a second generation TWIMS device, such as that used here, dissociation from ion heating was observed upon injection of ions into the TWIMS device, and the effective temperature of the ions decreased with increasing wave velocity [47, 48]. In addition, the ratio of folded to unfolded ubiquitin 6+ conformers depends on some parameters [47, 54] but not on the wave height or wave velocity . Thus, excess ion heating should not occur at the higher wave velocities used here during TWIMS. It is possible that ion heating upon injection may result in destabilization and subsequent unfolding of the ions during TWIMS with more unfolding occurring at the higher wave velocities owing to the longer drift times and thus more time for unfolding to occur. It is also possible that other high order factors, such as the time required to achieve force-balance, the rise time of the power supply, or effects from the confining rf also play a role. Higher m/z ions, such as those formed from buffered aqueous solutions, may experience more of these higher order factors, such as a greater extent of the population slightly off the central axis and thus exposed to different electric fields. Interestingly, data for Cs+ indicate that the cross-section varies by less than 1.0% with the same range of wave heights and wave velocities used for the protein data. Cs+ cannot undergo a conformational change and appears to be unaffected by these other high order factors. It is also unclear how these other factors would result in longer transit times for folded protein ions than for unfolded protein ions with similar adjusted cross-sections. Thus, conformational changes may play a role in the protein data.
In summary, the results in Figure 5 indicate that computational calibration of TWIMS can be used to obtain absolute collisional cross-sections of protein and peptide ions formed from both denaturing and buffered aqueous solutions that are similar to those obtained with DTIMS, but that low wave velocities and gentle instrument settings should be used to minimize any uncertainties resulting from high-order effects not accounted for in the present model and from any unfolding that might occur.
A method for calibrating TWIMS drift times using computational simulations in order to obtain collisional cross-sections is presented. The accuracy of this method is assessed by comparing the collisional cross-sections of 70 different reference ions obtained using this method with those reported from DTIMS measurements. The cross-sections obtained here with low wave velocities are very similar to those obtained with DTIMS (average difference = 0.3%), both for ions formed from denaturing solutions and for those formed from buffered aqueous solutions. These results demonstrate that collisional cross-sections can be obtained from a single TWIMS drift time measurement without prior experimental calibration. The method presented here does not include a discrete description of the collision events that occur between the ions and the buffer gas nor does it account for the identity of the buffer gas. This significant limitation of the model could be improved by including a term describing the intermolecular potentials between the ions and the buffer gas. This improvement would make it possible to extend this method for use with a variety of buffer gases. This method also does not include corrections for surface topology  or pressure gradients along the axis of the device. Moreover, a rough approximation that force-balance is achieved instantaneously is made in the derivation of this model. Despite these significant deficiencies, the uncertainty in the collisional cross-sections obtained using this method is about the same as that obtained using the more conventional TWIMS experimental calibration approach. Therefore, this technique can eliminate the need for experimental calibration, although further experiments are needed to determine the effects of other variables, such as pressure, bias voltage, and scan frequency, on the accuracy of this method.
The collisional cross-sections of protein and peptide ions obtained here with high wave velocities are larger than those obtained with DTIMS, especially for those formed from buffered aqueous solutions. These higher than expected cross-sections could be the result of high-order effects not accounted for in the present model. Data obtained with high wave velocities (≥1000 m/s) for the ions formed from buffered aqueous solutions may also be consistent with the protein ions unfolding during TWIMS. These results indicate that low wave velocities should be used for obtaining collisional cross-sections with TWIMS in order to minimize any uncertainties that may result from high-order effects or from changes in protein ion conformation that can occur during TWIMS. The resolution of TWIMS measurements increases with increasing wave velocity . Therefore, a balance must be struck between resolution and accuracy when selecting the TWIMS wave velocity. The accuracy of the TWIMS computational calibration cross-sections also depends on the accuracy to which the pressure inside the TWIMS cell is known. It should be possible to calibrate the pressure in a TWIMS drift cell by measuring the drift time of an ion that will not likely undergo a conformational change during TWIMS, such as C60  or bovine pancreatic trypsin inhibitor . The pressure used to calculate the drift time of such an ion can be varied until a value similar to the measured drift time is obtained. With a calibrated pressure, adjusted collisional cross-sections can be obtained with TWIMS by computing drift times using purely hypothetical adjusted cross-sections in order to obtain a second-order polynomial function that relates drift times to adjusted cross-sections. The range of adjusted cross-sections in these calculations should be chosen so as to bracket the measured drift times to be calibrated. The absolute cross-section can be obtained from the adjusted cross-section with the reduced mass and ion charge. The latter can be readily obtained when isotopic resolution is achieved or from the m/z spacing between molecular ions in less complex samples.
The authors thank the reviewers of this manuscript for thoughtful comments and suggestions, the UCSF Sandler-Moore Mass Spectrometry Core Facility for use of their Synapt G2 instrument, and the National Institutes of Health for funding (R01GM097357 and S10OD020062). The authors are also thankful for the pioneering contributions made by Professor Scott A. McLuckey in the fields of mass spectrometry instrumentation and methods development and gas-phase ion chemistry.
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