Article pubs.acs.org/ac
Molecular Structures and Ion Mobility Cross Sections: Analysis of the Effects of He and N2 Buffer Gas Christian Bleiholder,† Nicholas R. Johnson,‡ Stephanie Contreras,∥ Thomas Wyttenbach, and Michael T. Bowers* Department of Chemistry and Biochemistry, University of California Santa Barbara, Santa Barbara, California 93106, United States S Supporting Information *
ABSTRACT: An empirically observed correlation between ion mobility cross sections in helium and nitrogen buffer gases was examined as a function of temperature, molecular size, and shape. Experimental cross sections were determined for tetraglycine, bradykinin, angiotensin 2, melittin, and ubiquitin at 300 K and in the range from 80 to 550 K on home-built instruments and calculated by the projection superposition approximation (PSA) method. The PSA was also used to predict cross sections for larger systems such as human pancreatic alpha-amylase, concanavalin, Pichia pastoris lysyl oxidase, and Klebsiella pneumoniae acetolactate synthase. The data show that the ratio of cross sections in helium and nitrogen depends significantly on the temperature of the buffer gas as well as the size and shape of the analyte ion. Therefore, the analysis of the data indicates that a simple formula that seeks to quantitatively relate the momentum transfer cross sections observed in two distinct buffer gases lacks a sound physical basis.
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This approach is justified by an empirically observed strong and linear correlation between helium and nitrogen cross sections.13,22,23 Bush et al. reported that ion mobility data recorded in nitrogen can be converted into effective helium cross sections with only small errors on average.22 However, these publications also indicate that the quality of the correlation between ion mobility data recorded in helium and nitrogen buffer gases depends on molecular properties, such as molecular charge or size, and suggest that the ion-neutral interaction potential has an influence on the quality of the correlation. Therefore, while a qualitative correlation of cross section data obtained in helium and nitrogen buffer gases is not in dispute, there appears to be a substantial lack of knowledge regarding the physical basis of this empirically observed correlation between helium and nitrogen ion mobility data that is currently at the core of applying IMS-MS for structure elucidation. In this work, we address this lack of insight by investigating the effects of buffer gas temperature and analyte size and shape on the relationship between momentum transfer cross sections in nitrogen and helium buffer gases on select model systems by a combined computational and experimental approach.
on mobility spectrometry-mass spectrometry (IMS-MS) is a versatile structure-elucidation method that simultaneously determines mass and shape of an analyte. IMS-MS instruments directly evaluate the arrival time of a mass-selected ion drifting through a buffer gas under the influence of a weak electric field and provide therefore a measure for the ion mobility K and the momentum transfer cross sectional area Ω of the analyte ion.1 Detailed structural information on the analyte ion can be obtained when the ion mobility-based collision cross section (CCS) Ω is compared to cross sections computed for candidate model structures.2,3 This generic approach has been widely utilized to determine structures of small inorganic compounds, such as carbon or metal clusters,2−4 self-assembling materials,5 and a wide array of biological macromolecules and their assemblies,6−9 including amyloid fibrils10 and viral capsids.11 Thus, two components are required in order to use IMS-MS as a structure elucidation technique: one experimental component to determine the CCS of the analyte and a second computational component to assign a structural model to the experimental IMS-MS cross section. However, IMS-MS instrumental platforms and the computational methods needed for structure-elucidation by IMS-MS have largely developed on separate paths. As a consequence, arrival time distributions (ATDs) are predominantly recorded in nitrogen buffer gas12−14 while the computational approaches were developed for use with helium.15−19 Therefore, the widely applied approach to obtain a molecular structure from an IMS arrival time is to use a calibration procedure converting measured nitrogen CCS data into effective helium cross sections and subsequently utilize the theoretical tools developed for helium buffer gas to deduce the molecular structure.11,20,21 © XXXX American Chemical Society
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EXPERIMENTS Ion Mobility Measurements. Stock solutions of 18Crown-6 (with or without sodium or potassium salt added), tetraglycine, and other peptides were prepared in 50:50 water/ Received: March 19, 2015 Accepted: June 13, 2015
A
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Figure 1. Ion mobility data in nitrogen (blue) and helium (green) for Gly4H+. (a) Arrival time distribution (ATD) for Gly4H+ at 300 K in nitrogen buffer gas. A single peak with diffusion-limited width is observed. (b) Two minor satellite peaks (indicated by arrows) emerge in the ATD at 80 K. (c) Experimental (x symbols) and theoretical cross sections (dots) of Gly4H+ in helium and nitrogen buffer gases in the temperature range from 80 to 700 K. The cross sections increase in both drift gases when the temperature is decreased due to an increased significance of glancing collisions at lower thermal energy. However, the CCS increase is more pronounced in nitrogen than in helium buffer gas due to a deeper and longer-range “attractive well” of the ion-nitrogen interaction potential.
methanol as previously described.17 These solutions were diluted to the desired concentration (typically 10−100 μM) and loaded into gold coated nanoelectrospray ionization (ESI) capillaries used in the IMS-MS experiments. The home-built IMS-MS instrumentation has been described in detail elsewhere.24 Briefly, the instrument is comprised of a nano-ESI source, an ion funnel, a temperature controlled drift cell, a quadrupole mass analyzer, and an electron multiplier detector. The desolvated ions are collected, focused, and stored in the ion funnel located in front of the drift cell. A 10 μs pulse of ions is injected into the 5 cm drift cell filled with ∼5 Torr of helium or ∼1.5 Torr of nitrogen gas through which they gently drift under the influence of a weak electric field (5−20 V/cm). The injection energy is kept as low as possible to minimize collisional heating of the ions during the injection process. Following the drift cell, the ions are mass analyzed with a quadrupole mass filter and detected with a traditional conversion dynode/electron multiplier arrangement. Arrival times ta are recorded at different drift voltages V (∼90, 50, 40, and 30 V) and are plotted as a function of the ratio p/V where p is the buffer gas pressure.25 The ion mobility K is obtained from the slope of the plot and converted into a cross section Ω (see below). Ω values were measured in the temperature range from approximately 77 to 550 K, averaged over three independent measurements. Two 10 μM sample solutions were prepared for ubiquitin, an acidic solution containing 1% acetic acid and a pH-neutral solution, with the solvent being a 1:1 mixture of methanol and water in both cases. Temperature-dependent experiments were carried out as described above. Additional 300 K experiments were carried out on a high-resolution IMS-MS instrument described previously.26 In this setup, the drift tube is two meters long and its temperature cannot be changed. A second major difference is the introduction of the ions into the drift region. Whereas ions undergo an injection process from vacuum into the drift cell in the temperature-variable instrument, they gently drift at essentially a constant pressure of ∼10 Torr through an ion funnel from the source into the drift tube. This gentle ion transfer is more suitable to keep ions
kinetically trapped in a solution-like conformation. The nanoESI source itself is identical on both instruments. Neutral ubiquitin solutions yield good intensity for charge states 6+ to 8+ on both apparatuses, whereas for acidic solutions the intensity shifts to charge states 10+ to 13+. Collision Cross Section Calculations. Structures of tetraglycine and the 18-Crown-6 ethers were taken from previous publications.17,19,27 Briefly, the structures had been derived from initial molecular dynamics (MD) calculations using the Amber03 force field.28 In these calculations, the trajectory is propagated for 10 ns with the temperature repeatedly varied from 1000 K to below 200 K in time steps of 4 ps with exponential cooling (λ = 0.85). A harmonic restraint with a force constant of 20 kcal/mol on amide group dihedrals was applied during the dynamics to prevent trans → cis isomerization. This procedure yielded 2500 candidate structures for further geometry optimization at the PM3, RHF/3-21G*, B3LYP/6-31G*, and finally B3LYP/6-31+G** levels of theory using the Gaussian03 suite of programs. At each step, structures were grouped into conformational families based on dihedral angles and only the lowest energy structure was used for further refinement. The structure for the ubiquitin native state is the AMBER energy minimized structure of the NMR structure26 while the ubiquitin A-state was assembled by molecular mechanics by Segev et al.29 The crystal structure of Klebsiella pneumonia acetolactate synthase30 and other protein complexes were downloaded from the protein data bank (PDB, entries 1OZG, 1KBK, 1JBC, 1NGE) and modified as described.17 In particular, hydrogen atoms were added and solvent/counterions removed. Projection superposition approximation (PSA) calculations in helium buffer gas were performed as described previously. A novel parameter set was derived in the current work for using the PSA method in conjunction with nitrogen ion mobility data. The parameter calibration procedure was identical to the one used to derive the helium parameter set (see the Supporting Information for details). If applicable, cross sections were calculated using the standard sigma projection19 and more rigorous trajectory18 methods for comparison with our new PSA method on the same molecular B
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Analytical Chemistry structures. The PSA method is available free of charge (see https://labs.chem.ucsb.edu/bowers/michael/).
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RESULTS Experimental and theoretical cross section data for both helium and nitrogen buffer gases are compiled in Tables S1−S6 in the Supporting Information. The present study includes experimental data for a range of peptides and the small protein ubiquitin along with theoretical PSA data for selected examples, including several large proteins and protein complexes. In the following sections, we focus on data for three extreme examples: tetraglycine, ubiquitin, and Klebsiella pneumoniae acetolactate representing a small biomolecule, a protein, and a large protein complex, respectively. Tetraglycine. A single narrow peak is observed in the ion mobility spectrum for protonated tetraglycine in nitrogen buffer gas. The symmetrical and narrow peak in Figure 1a indicates that all Gly4H+ ions populate just one and the same conformation, that the structures populated are so similar that they cannot be distinguished by cross section, or that different conformations rapidly interconvert. Some evidence for the population of more than one conformation, which either coexist or rapidly interconvert at room temperature, is provided by the data recorded in nitrogen buffer gas at 80 K (Figure 1b). At this low temperature, one rather narrow peak dominates the ATD but subtle shoulders to the left and right of the main peak are visible, indicating coexisting additional conformations. However, irrespective of the extent of dynamics in Gly4H+ as a function of temperature, the 80 K nitrogen data maintain clearly that there is very little structural diversity for this small peptide in terms of cross section, in line with our previous investigations using helium buffer gas.19 Our computational results further support the view of one folded conformation prevailing for Gly4H+ (see Figure S4 in the Supporting Information). Figure 1c compares the CCS recorded in nitrogen and helium for Gly4H+ to the predictions by the PSA method as a function of temperature. First, we note that the fitted PSA parameters are of high quality in terms of reproducing the temperature dependency of the cross section in helium and nitrogen buffer gas. Second, we note that the slope of the cross sections as a function of temperature is much larger for nitrogen than it is for helium as buffer gas. While the experimental CCS increases by about 55% when decreasing the temperature of the helium buffer gas from ∼550 to 80 K, the CCS measured in nitrogen increases by about 205% in the same temperature regime. Ubiquitin. Previous IMS work26,31−33 indicates that the ATDs recorded for this protein depend on the charge state and, to some degree, on sample and source conditions. In contrast to the simple ATDs of tetraglycine, those of ubiquitin can be quite complex displaying several features. The features can be grouped into a sharp peak at a short drift time observed for low charge states and a series of sharp peaks at long times observed for higher charge states. Many ATDs also show in addition to the sharp peaks a broad feature at intermediate drift time. The ATD recorded in nitrogen buffer gas at 300 K for ubiquitin charge state 8+ presented in Figure 2a shows all three features at short, intermediate, and long drift time simultaneously. Previous work indicates that the sharp peak at short drift time (yellow area in Figure 2a) must be due to a native-like structure whereas the peak at longer drift time (orange area in Figure 2a) corresponds to a structure which is about as compact as the A-
Figure 2. Ion mobility data in nitrogen and helium for ubiquitin. (a) ATD of ubiquitin 8+ charge state in nitrogen buffer gas at 300 K. Peaks used for comparison with theoretical native state and A-state data are highlighted in yellow and orange, respectively. (b) Experimental cross section data (triangles) for the native (N) state (charge states 6+ to 8+) and the A-state (charge states 8+ to 11+) and PSA theoretical cross section data (dots) in nitrogen (blue) and helium (green).
state.26,33 Cross sections for charge states 9+ to 13+ indicate the A-state is more and more unfolded with increasing charge. In fact, the charge state 13+ structure is found29,34 to be significantly extended with no A-state-like secondary structure left (see Figure S3 in the Supporting Information). Nevertheless, for simplicity, the collection of sharp peaks at long drift times observed for charge states 8+ to 13+ is sometimes called the A-state data set in the remainder of this work. Figure 2b compares the CCS deduced from the sharp peaks in the 300 K ATDs observed for the ubiquitin charge states 6+ to 11+ in nitrogen and helium to the theoretical cross sections predicted by the PSA method for the native state and the Astate. First, we again note that the CCS predictions made by the PSA method are in overall agreement with the experimental values at 300 K for the 6+ to 11+ charge states. In line with our observations made for Gly4H+ in the previous section, we further note that for both the native state and the A-state the (PSA-predicted) increase in cross section when decreasing the temperature is larger for nitrogen (95% and 92%, respectively) than for helium (13% and 18%, respectively) buffer gas. Klebsiella pneumoniae Acetolactate Synthase. The Klebsiella pneumoniae acetolactate synthase crystal structure (PDB entry 1OZG)30 is used here as a model system to study buffer gas and temperature effects by PSA calculations for a large protein complex (240 kDa molecular weight). The CCS values in nitrogen are found to increase by about 30% when the temperature is decreased from 600 to 80 K (Figure S1 in the Supporting Information) while the predicted increase in helium cross sections is only 3% to 5% for the same temperature range. Thus, the PSA-predicted changes in CCS for Klebsiella pneumonia acetolactate synthase are significantly smaller than for the ubiquitin and tetraglycine systems discussed above. C
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DISCUSSION General Remarks on the Collision Cross Sections and the Analyte-Buffer Gas Interaction. As an analyte ion travels through the ion mobility drift cell under the influence of a weak electric field, it undergoes hundreds of thousands to millions of collisions with buffer gas particles depending on system parameters. The ion mobility K is given by the momentum transfer integral Ω arising from these collisions K=
3e 16N
2π 1 μkBT Ω
transfer observed in distinct buffer gases should reflect details of the molecular and electronic structure of the analyte ion. For the remainder of this work, we seek to demonstrate this point of view by investigating the interplay between molecular size, molecule shape, and temperature on the momentum transfer cross section by experimental and computational methods. Effect of Temperature on the Momentum Transfer Cross Section. Figure 1c shows that the CCS of Gly4H+ increases significantly with decreasing temperature. However, the effect is much more pronounced for nitrogen with a 205% increase from 550 to 80 K compared to just 55% for helium. Consequently, the cross section determined at 80 K in nitrogen (357 Å2) is nearly three times as large as the cross section in helium (121 Å2) while at 500 K the cross section in nitrogen is only approximately 50% larger than that in helium. A change in temperature can modify the observed CCS in two different ways. First, a change in temperature can change the prevalent conformation for the analyte ion and thus indirectly change the observed CCS via changing the molecular structure. Such an indirect effect is highly system-specific and has been observed, e.g., for polymeric compounds19,37 and small nucleotides.38,39 The data recorded for Gly4H+ indicate only marginal structural diversity because the widths of the peaks in the ATD are largely determined by diffusion from 80 to 550 K (see above). The experimental data thus indicate that the changes in cross sections observed in Figure 1c are not due to conformational changes of Gly4H+ when increasing the buffer gas temperature. In addition, the Gly4H+ structure is characterized by a strong hydrogen bond between N- and Ctermini (see Figure S4 in the Supporting Information) which is expected to break at high temperature (if at all), thereby leading to an increase of the cross section as temperature rises, not a decrease as observed. Another mechanism, by which a change in temperature can directly affect the CCS, is by defining the thermal energy available for the collision process. The lower the kinetic energy (i.e., the lower the temperature), the more significant are the contributions from glancing collisions to the collision process. In particular, long-range effects of the attractive “well” of the interaction potential U(r)⃗ dominate the collision process only at lower temperature. However, with increasing kinetic energy, i.e., increasing temperature, the repulsive wall of the interaction potential increasingly influences the collision process at the expense of the long-ranging attractive part. The reader is referred to the literature for an in-depth discussion of the collision process.1,18,35 Here, we will simply note that with increasing temperature collisions “occur” increasingly closer to the atomic center, resulting in a decrease in CCS with increasing temperature. This effect of temperature on the CCS is independent of any molecular dynamics and has previously been observed most notably for the structurally rigid C60+ system.19 The data thus indicate that this increase in CCS with decreasing temperature shown in Figure 1c for Gly4H+ arises from this mechanism. The structures computed for Gly4H+ indicate that the overall shape of the Gly4H+ ion can to a first approximation be considered a sphere. Therefore, the data in Figure 1c can readily be converted into effective collision radii, r = (Ω/π)1/2, and at 80 K, the Gly4H+-He collision radius is found to be 4.5 Å smaller than the Gly4H+-N2 radius (Table S7 in the Supporting Information). At 500 K, on the other hand, the difference is only 1.1 Å, a value which approaches the nitrogen-helium difference in van der Waals radii of ≤0.7 Å (Table S7 in the Supporting Information).40 Thus, we conclude
(1)
where T is the buffer gas temperature, μ the reduced mass, e the ion charge, N the gas number density, and kB the Boltzmann constant.1 Ω is determined by the probability distribution of deflection angles p(ε, θ) by which a buffer gas particle with kinetic energy ε is deflected upon a collision with the ion. Ω(T ) =
∫0
∞
dε
∫0
π
dθ f (ε , T )p(ε , θ )(1 − cos θ )
(2)
Here, the term f(ε, T) denotes the Boltzmann energy distribution and the term (1 − cos θ) corresponds to the relative momentum transfer for a collison with deflection angle θ. It is important to note that the deflection angle θ is entirely defined by the kinetic energy ε of the collision process and the intermolecular forces between the analyte ion and the buffer gas particle, U(r )⃗ . 35 Thus, the interaction potential U(r )⃗ determines the ion mobility cross section for a given temperature. For this reason, differences in CCS between measurements in helium and nitrogen drift gases directly reflect differences in the analyte-buffer gas interaction potential for helium, Uhelium(r)⃗ , and nitrogen, Unitrogen(r)⃗ . For the systems investigated here, the attractive part of the ion-buffer gas interaction is dominated by an induction-type interaction arising from the static polarizability α of helium and nitrogen buffer gases. The polarizability of nitrogen (expressed by its polarizability volume α′ = 1.74 Å3) is nearly an order of magnitude larger than that of helium (α′ = 0.205 Å3).1 As a consequence of this much stronger polarizability of nitrogen, the ion-nitrogen potential well is much deeper.36 In addition, the repulsive potential wall is shifted to larger distances than in the ion-helium potential (Figure S5 in the Supporting Information). Due to these differences in the interaction potential, the deflection angle distributions in helium, pHe(ε, θ), and nitrogen drift gases, pN2(ε, θ), differ from each other (for identical analyte ion and identical buffer gas temperature), leading in general to a larger momentum transfer cross section for nitrogen than for helium buffer gas. The exact form of the ion-buffer gas interaction potentials Uhelium(r)⃗ and Unitrogen(r)⃗ , however, depends decisively on the exact molecular structure of the analyte ion (e.g., shape and size) and also the electronic state (e.g., charge distribution). Thus, a generic relationship between the interaction potentials of distinct molecules A (UAhelium(r)⃗ and UAnitrogen(r)⃗ ) and B B B (Uhelium (r)⃗ and Unitrogen (r)⃗ ) does not exist, and as a consequence, there is no rigorous relationship between the corresponding deflection angle distributions pA,B helium,nitrogen(ε, θ), either. Therefore, a general formula that seeks to quantitatively relate the ratio of the momentum transfer cross section of molecule A observed in helium to that in nitrogen buffer gas, ΩAN2/ΩAHe, to the cross section ratio of molecule B, ΩBN2/ΩBHe, lacks a sound physical basis. Rather, the ratio of momentum D
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Analytical Chemistry first that the collision process is dominated by the repulsive wall at high temperature (since the van der Waals radii are based on neutral-neutral interactions where attractive terms are very small) and second that the deep attractive well of the nitrogen interaction potential significantly contributes to the CCS especially at low temperature. Effect of Molecular Size and Temperature on the Momentum Transfer Cross Section. However, whereas the attractive well of the interaction potential U(r)⃗ is very important for small molecules such as Gly4H+, it increasingly loses in significance as compounds increase in molecular weight and size and the CCS is increasingly determined by the repulsive wall (see Figure S6 in the Supporting Information). Hence, the interaction potential can be approximated by a hardbody potential as compounds approach bulk matter. As a consequence, the effect of temperature on the CCS is expected to be less pronounced and CCS values are less dependent on the choice of buffer gas with increasing molecular weight of the analyte. These effects are evident in Figure 3 which displays data for three different analytes with masses of 0.25, 8.6, and 240 kDa.
temperature and buffer gas on the CCS decreases with increasing molecular weight of the analyte. Temperature Effect with Different Molecular Shapes. The shape of an analyte ion can also affect its interaction potential with the buffer gas (Figure 4) and thus influence the
Figure 4. Illustration how the shape of the analyte ion influences the differences in cross section measured in distinct buffer gases with different sizes (i.e., interaction potentials).
relative difference between momentum transfer cross sections determined in different buffer gases in addition to temperature and molecular weight of the analyte. For example, a rod-like analyte ion interacts with the buffer gas through a larger surface area than a sphere-like ion. Hence, a rod-like ion (such as charge state 13+ of ubiquitin) is expected to experience a larger change in cross section than a sphere-like ion (such as the native state of ubiquitin) when the buffer gas is changed. A similar buffer gas effect is anticipated for analyte ions with a strong surface roughness and molecular cavities present in many protein systems compared to an ion without cavities. Here, a weakly interacting buffer gas, such as helium, is expected to sample the molecular surface more finely than a more strongly interacting one, such as nitrogen. For rough, nonconvex molecular shapes with significant cavities and voids, differences in momentum transfer cross section when changing buffer gases are therefore expected to be more significant than for smooth, convex shapes. In the discussion of the temperature effect in the preceding section, it was noted that the relative increase in cross section when switching the buffer gas from helium to nitrogen was different for the ubiquitin native state compared to the A-state. Here, we will take a closer look at this effect. The relative change in CCS, (ΩN2 − ΩHe)/ΩHe, is predicted (based on PSA) to be larger for the A-state (20%) than for the N-state (6%) at the high temperature end of our study. Since it is the repulsive wall that dominates the collision process in this temperature regime, the observed difference in (ΩN2 − ΩHe)/ΩHe reflects the difference between the molecular surface areas relevant in the repulsive interaction with the buffer gas for the native state and the A-state. The PSA method computes not only the cross sectional area Ω but, by doing so, also the area A of the molecular surface exposed for collisions with the buffer gas particles. This computed surface area is for the globular native state (ANmol(He, 600 K) = 3306 Å2) substantially smaller than for the extended A-state (AAmol(He, 600 K) = 5470 Å2).
Figure 3. Cross section Ω as a function of temperature normalized by the 300 K cross section for tetraglycine, ubiquitin, and acetolactate synthase in helium (top) and nitrogen buffer gas (bottom). Circles indicate experimental data, crosses theoretical PSA data. Tetraglycine is measured in its singly protonated form, ubiquitin in charge state 7+. The ubiquitin PSA data (used to supplement the experimental data) include both native and A-state structures which show a very similar temperature dependence.
For the smallest ion, Gly4H+, the CCS in nitrogen and helium increases by approximately a factor of 2.3 and 1.5, respectively, when decreasing the temperature from 300 to 80 K, whereas the cross section for the 8.6 kDa-protein ubiquitin increases only by about factors of 1.5 and 1.2 in nitrogen and helium, respectively. For the largest analyte, acetolactate synthase, the PSA method predicts the CCS to increase from 300 to 80 K by only 26% and 3% in nitrogen and helium, respectively. Our data also indicate that buffer gas effects decrease with increasing molecular weight: While the CCS of Gly4H+ at 500 K increases by approximately 50% when the buffer gas is switched from helium to nitrogen (Figure 1c), this increase in cross section is predicted to decrease to about 6% and 20% for the N- and A-states of ubiquitin, respectively, (Figure 2b) and further to approximately 3% for acetolactate synthase. In summary, the data show that the significance of both E
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Figure 5. Comparison of 300 K ion mobility data obtained in helium and nitrogen buffer gases. (a) Correlation between experimental helium and nitrogen cross sections for the native (N) state (charge states 6+ to 8+) and the A-state of ubiquitin (charge states 8+ to 13+). Cross sections increase with increasing charge state. Linear regression models based on the native state (solid line) and the A-state (dashed line) are included. (b) Relative difference (ΩN2 − ΩHe)/Ω between nitrogen and helium cross sections as a function of the helium cross section. Included are data from Bush et al.23 (blue triangles) and a fit (green line) to our experimental and computed data (excluding the ubiquitin A-state). Please see Figure S2 in the Supporting Information for more details.
buffer gas from helium to nitrogen than for a globular structure. On the basis of a simple geometrical argument in two dimensions, this is expected: If the effective buffer gas particle radius is 2 Å larger for nitrogen than for helium, we anticipate for a spherical ion approximately the size of ubiquitin (r = 20 Å) a cross section increase of 264 Å2, whereas an ion of the same size but with a cross sectional aspect ratio of 1:4 yields a 30% larger increase of 347 Å2. The 2020 Å2 helium cross section for ubiquitin charge state 13+ (Table S4 in the Supporting Information) and the 640 Å2 increase when switching from helium to nitrogen indicate an aspect ratio for this system of about 1:10. While we emphasize that these geometrical arguments strictly hold only for two dimensions, we note that the extended ubiquitin model structure shown in Figure S3 in the Supporting Information is qualitatively in good agreement with such an extreme aspect ratio. It is noted that the ion mobility data for the ubiquitin A-state deviate increasingly more from the spherical trend line with increasing charge state, because the ubiquitin conformation becomes increasingly extended (less spherical) due to Coulomb repulsion. It is further noteworthy that the IMS data reported by Bush et al. on a large number of biological systems23 agree very well with the spherical trend line based on our fitted value δReff = 1.93 Å, with the notable exception of the higher charge states of ubiquitin and cytochrome C (Figure 5b). Thus, in agreement with our data, the buffer gas effect is magnified for the extended, A-state-like ubiquitin structures compared to the more spherical native state structure. Whereas the shape effects discussed above are caused by the overall geometry of the ion (spherical vs extended), the local makeup of the ion surface, the surface “roughness”, also contributes to a buffer gas-dependent effect on the cross section. Ion structures with rough surfaces appear more convex using a large buffer gas particle, since structural details, such as small dents, are not sampled by a large probe particle (see Figure 4). Convex particles transfer on average less momentum in a collision and have therefore a smaller momentum transfer cross section than their concave counterparts.15,16 As pointed out earlier, two effects contribute to the effective size of a buffer gas particle: the position of the repulsive wall and the depth of
Figure 5a correlates the experimental cross sections recorded in nitrogen ΩN2 to those recorded in helium buffer gas ΩHe. Overall, a linear relationship can be established (see the Supporting Information for details), in line with previous reports.13,22,23 However, a closer look at Figure 5a shows that a linear regression model ΩN2 = m × ΩHe + a established for the A-state data set does not quantitatively explain the relationship between the nitrogen and helium cross sections for the native state. In fact, the nitrogen cross sections measured for the native state (charge states 6+ to 8+) are approximately 40% larger than expected from the correlation observed for the Astate (charge states 8+ to 13+). Obviously, addition or subtraction of a charge has a different effect on the cross section within the data set assigned to compact native-like structures compared to the set of extended A-state-derived conformations. Our analysis above indicates that the molecular shape clearly influences the difference in CCS when switching the buffer gas from helium to nitrogen. Consequently, we expect the ratio (ΩN2 − ΩHe)/ΩHe to contain information about the shape of the analyte ion. Figure 5b correlates the relative increase in cross section (ΩN2 − ΩHe)/ΩHe with the helium cross section ΩHe. As shown in the Supporting Information, Section 2, (ΩN2 − ΩHe)/ΩHe is related to ΩHe by Ω N2 − Ω He Ω He
=
π ·δR2 2 π ·δR + Ω He Ω He
(3)
for ideal hard spheres where δR is the difference between the helium and nitrogen radii. As we point out in the Supporting Information, an effective difference δReff = 1.93 Å (at 300 K) can be fitted to make eq 3 match our ion mobility data for globular analyte ions (Figures 5b and S2 in the Supporting Information). The data used for the fitting include experimental ion mobility data of small peptide ions and the ubiquitin native state, as well as PSA-predicted data on larger protein systems. Figure 5b reveals that the ubiquitin A-state data are located above the spherical trend line indicating that the cross section of extended molecular structures is more affected by a switch of F
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Analytical Chemistry Author Contributions
the potential well (Figure S5 in the Supporting Information). The surface roughness effect is hard to quantify experimentally, but theoretical methods such as PSA readily expose it. The PSA shape factor is a measure of the concavity of a given ion shape which increases the momentum transfer cross section compared to a fully convex reference shape.16 Convex shapes have a shape factor of 1 whereas concave surface elements increase the shape factor to values greater than 1. Table 1
The manuscript was written through contributions of all authors. All authors have given approval to the final version of the manuscript. Notes
The authors declare no competing financial interest.
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ACKNOWLEDGMENTS We gratefully acknowledge the support of the National Science Foundation under grant CHE-1301032 and the Air Force Office of Scientific Research under grant FA9550-11-1-0113.
Table 1. Calculated PSA Shape Factor for a Number of Biomolecules Using Helium or Nitrogen Buffer Gas
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PSA shape factor bradykinin ubiquitin pancreatic α-amylase acetolactate synthase
mass (kDa)
helium
nitrogen
1.1 8.6 56 240
1.056 1.184 1.258 1.453
1.043 1.142 1.174 1.407
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summarizes theoretical PSA shape factor values for a number of molecular structures studied in this work. It can be seen that all structures appear more convex (yielding smaller shape factors) using nitrogen buffer gas compared to helium. Hence, structural details are lost using nitrogen.
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SUMMARY AND CONCLUDING REMARKS Our analysis shows that ion mobility data acquired in different buffer gases are functionally not rigorously related but instead to some extent complementary. Therefore, a general formula that seeks to quantitatively relate the ratio of the momentum transfer cross sections observed in helium to that in nitrogen buffer gas without considering the experimental parameters (such as temperature, molecular shape, charge state, etc.) lacks a sound physical basis. For this reason, caution is warranted if ion mobility data recorded in nitrogen, or other buffer gases like CO2, are converted to helium ion mobility data when used for structure analysis.
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ASSOCIATED CONTENT
S Supporting Information *
Tables of experimental and computed cross sections, a discussion of a hard sphere model, figures of model structures used in this work, data presenting properties of the interaction between two particles, and a description of the PSA fitting procedure. The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/ acs.analchem.5b01429.
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REFERENCES
AUTHOR INFORMATION
Corresponding Author
*E-mail:
[email protected]. Present Addresses †
C.B.: Department of Chemistry and Biochemistry and Institute of Molecular Biophysics, Florida State University, Tallahassee, Florida 32306−4390. ‡ N.R.J.: Department of Chemistry and Biochemistry, University of Colorado at Boulder, Boulder, Colorado 80309. ∥ S.C.: Department of Chemistry, University of California at Davis, One Shields Ave, Davis, California 95616. G
DOI: 10.1021/acs.analchem.5b01429 Anal. Chem. XXXX, XXX, XXX−XXX
Article
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DOI: 10.1021/acs.analchem.5b01429 Anal. Chem. XXXX, XXX, XXX−XXX
