Effects of Charge State, Charge Distribution, and Structure on the Ion

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Effects of Charge State, Charge Distribution, and Structure on the Ion Mobility of Protein Ions in Helium Gas: Results from Trajectory Method Calculations Kenneth J. Laszlo and Matthew F. Bush* University of Washington, Department of Chemistry, Box 351700, Seattle, Washington 98195-1700, United States S Supporting Information *

ABSTRACT: Collision cross section (Ω) values of gas-phase ions of proteins and protein complexes are used to probe the structures of the corresponding species in solution. Ions of many proteins exhibit increasing Ω-values with increasing charge state but most Ω-values calculated for protein ions have used simple collision models that do not explicitly account for charge. Here we use a combination of ion mobility mass spectrometry experiments with helium gas and trajectory method calculations to characterize the extents to which increases in experimental Ω-values with increasing charge state may be attributed to increased momentum transfer concomitant with enhanced long-range interactions between the protein ion and helium atoms. Ubiquitin and C-to-N terminally linked diubiquitin ions generated from different solution conditions exhibit more than a 2-fold increase in Ω with increasing charge state. For native and energy-relaxed models of the proteins and most methods for distributing charge, Ω-values calculated using the trajectory method increase by less than 1% over the range of charge states observed from typical solution conditions used for native mass spectrometry. However, the calculated Ω-values increase by 10% to 15% over the full range of charge states observed from all solution conditions. Therefore, contributions from enhanced ioninduced dipole interactions with increasing charge state are significant but without additional structural changes can account for only a fraction of the increase in Ω observed experimentally. On the basis of these results, we suggest guidelines for calculating Ωvalues in the context of applications in biophysics and structural biology.

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INTRODUCTION Collision cross section (Ω) values of gas-phase ions of proteins and protein complexes determined from ion mobility (IM) mass spectrometry (MS) experiments1,2 have provided new insights into the assembly of amyloid fibrils,3,4 fibroblast growth factors,5 multiprotein enzymes,6 and virus capsids,7,8 as well as the dynamics of a rotary ATPase9 and small heat shock proteins.10 In those studies, experimental Ω-values were used to filter or guide the design of candidate structural models, which necessitates the need for accurate methods for calculating Ωvalues. Most Ω-values calculated for protein ions made use of simple collision models that can be evaluated rapidly, but do not explicitly account for charge. For example, in the projection approximation (PA),11 the neutral buffer gas and the atoms in the ion are all treated as spheres and the Ω value is evaluated numerically as the orientationally averaged, projected area of the ion-neutral pair.12 ΩPA values depend on the radii selected to represent the atoms, e.g., the temperature dependence of IM measurements of C60+ from 80 to 600 K can be explained using the projection approximation and temperature-dependent, atom−atom collision radii.13 The PA method has also been adapted for use with coarse-grained models, wherein each element of the model is represented by a sphere.1,14,15 The extremely low computational cost of the PA method makes it especially amenable to integration with molecular dynamics16 and integrative modeling,17 which can generate large numbers of candidate structures. © XXXX American Chemical Society

Several approaches have been pursued to improve the accuracy of calculated Ω-values, while maintaining modest computational costs. In the exact hard-spheres scattering (EHSS) method,18 the Ω-value is determined from the momentum transfer expected from hard-sphere collisions between the ion and neutral. ΩPA and ΩEHSS values are identical for convex shapes, but ΩEHSS values are systematically larger for concave shapes.18 Variations of the EHSS method have incorporated the possibility of diffuse/nonspecular scattering and inelastic scattering, which yield better agreement with Ω-values measured using N2 and O2 gases.19 Another approach is the projection superposition approximation method,20 in which the Ω value is determined from the “ion projection cross section for given (but temperature-dependent) atomic radii, cross section increase due to the superposition of atom−buffer gas interaction potentials, and cross section increase due to the deviation of the molecular shape from a fully convex body.”21 Protein ions for IM-MS experiments are usually generated using electrospray ionization, and Ω-values and/or distributions can be determined for each charge state observed. For protein ions generated from denaturing conditions, e.g., solutions containing organic solvent and with low pH, Ω-values can Received: August 15, 2017 Revised: September 10, 2017 Published: September 14, 2017 A

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The Journal of Physical Chemistry A depend strongly on charge state (z), which has been attributed primarily to differences in ion structure as a function of z.22−26 In contrast, the Ω-values of the lowest-z product ions formed by cation-to-anion proton transfer reactions of protein ions generated from denaturing conditions25−27 as well as ions of proteins and protein complexes generated from “native-like” solution conditions, e.g., aqueous 200 mM ammonium acetate,2,28 can depend weakly on z. Interestingly, the Ω of the highest-z protein ions generated from supercharging and denaturing solution conditions depend less on z than their lower-z counterparts.29 The relative contributions of differences in structure and differences in momentum transfer resulting from enhanced long-range ion/neutral interactions with increasing z remains unclear. The effects of ion charge can be treated explicitly using the trajectory (TJ) method30 in which Ω-values are determined by calculating the average momentum transfer for many trajectories simulated using a more accurate potential.31 For collisions with He, the potential, U, between the neutral and each of the n atoms in the ion is described using a LennardJones potential, which is attractive at long distances and repulsive at short distances, and an ion-induced dipole potential that is attractive over all distances:30,31

values in the context of applications in biophysics and structural biology.

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METHODS Experiments. Ub1 was purchased from Boston Biochem (Cambridge, MA) and C-to-N terminally linked Ub2 was purchased from Enzo Life Science (Farmingdale, NY). For denaturing conditions, proteins were dissolved into 70% methanol/30% water, which was adjusted to pH 2.0 with trifluoroacetic acid. For supercharging conditions, 15% by volume of propylene carbonate was added to the solutions for denaturing conditions.29 For native-like conditions, Ub2 was prepared in a solution of aqueous 200 mM ammonium acetate at pH 7. Final protein concentrations ranged from 8.5 to 20 μM. IM-MS data was acquired using a Waters Synapt G2 HDMS (Wilmslow, U.K.) modified with a radio frequency confining drift cell that enables the absolute determination of Ω-values.40,41 Electrokinetic nanoelectrospray ionization was used to generate protein cations, as described previously.42 The atmospheric-pressure interface of the instrument was elevated to 120 °C, which results in some heat transfer to the sample capillary.26 Most IM experiments were performed using the radio frequency confining drift cell with a 212 V drift voltage and 2 mbar He gas. Arrival-time distributions were converted to Ω distributions as described previously.25 Ω-values for Ub2 from native-like conditions were determined using a fielddependent method that was reported previously.40 Models. The native models of these protein were generated by modifying the PDB entries of Ub1 (1UBQ), Ub2 (3AXC), and ADH (5ENV). Incomplete side chains were replaced using the Dunbrack rotamer library43 and hydrogen atoms were added using the default settings (which aim to be reasonable for a solution with physiological pH) in Chimera v1.11.2.44 The energy-relaxed models were generated using the native models, the Amber force field,45 100 steepest-descent steps, and 10 conjugate gradient steps with a 0.02 Å step size for each step, as implemented in Chimera. Images of the native and energyrelaxed models are compared in Figure S1. α-helical and linear models of Ub1 and Ub2 were built using Chimera and the expected dihedral angles. Coulombic surfaces of selected models were calculated using Chimera and eq 2

n ⎡⎛ ⎞12 ⎛ ⎞6 ⎤ σ σ U (r ) = 4 ∑ εi⎢⎜ i ⎟ − ⎜ i ⎟ ⎥ ⎢ ⎥ d d ⎝ ⎠ ⎝ i⎠ ⎦ i ⎣ i

−

2 ⎡ n ⎛ n q y ⎞2 ⎛ n q z ⎞2 ⎤ qx ⎞ α ⎢⎛ ⎜⎜∑ i 3i ⎟⎟ + ⎜⎜∑ i 3i ⎟⎟ + ⎜⎜∑ i 3i ⎟⎟ ⎥ 2 ⎢⎣⎝ i di ⎠ ⎝ i di ⎠ ⎝ i di ⎠ ⎥⎦

(1)

where r is the position of the neutral relative to the center-ofmass of the ion. For each atom, i, ε is the depth of the well of the Lennard-Jones potential, σ is the finite distance at which the Lennard-Jones potential is zero, q is the charge, d is the Euclidian distance relative to r, and x, y, and z are the Cartesian coordinates relative to r. For collisions with N2, additional terms are included, e.g., the ion-quadrupole interaction and the orientation of the linear molecule during the collision.32,33 Due to the high computational expense of the TJ method, it has rarely been used to calculate Ω-values for ions of proteins and protein complexes.34 However, advances in computer hardware and faster implementations of the TJ method,19,35−38 have made these calculations far more tractable for structural models with many atoms. Previous evaluations of the contributions of ion-induced dipole interactions and charge distributions using the TJ method have used carbon clusters, e.g., fullerenes, as model systems.30,31 Here, we report Ω-values determined using the TJ method, atomic models of ubiquitin (Ub1), diubiquitin (Ub2), and alcohol dehydrogenase (ADH), and several methods for assigning charge distributions. We compare these values with those measured here using IM with He gas for Ub1 and Ub2 from denaturing and supercharging conditions and Ub2 from native-like conditions, as well as those measured previously for Ub1 and ADH from native-like conditions.28,39 These results provide insights into how ion-induced dipole interactions affect ΩTJ values, and the extent to which changes in experimental Ωvalues with increasing z may be attributed to increased momentum transfer concomitant with enhanced long-range interactions between the protein ion and He drift gas. On the basis of these results, we suggest guidelines for calculating ΩTJ

n

ϕ=

∑ i

qi ε0di

(2)

where ϕ is the electrostatic potential of a point on a surface 1.4 Å away from the nearest atom in the ion and ε0 is the distanceindependent dielectric constant, i.e. the permittivity of vacuum. Ω Calculations. TJ method calculations were performed using IMoS v1.06.19,35,36 ΩTJ values determined using IMoS are similar to those determined using MOBCAL (within 1%) but require approximately 2 orders of magnitude less time.38 Charge distributions were assigned using seven methods, which are summarized in Table 1 and described further in the Supporting Information. Each calculation used 10 000 gas trajectories in 199.98 Pa of He at 301.15 K and the LennardJones parameters used in the original version of MOBCAL.31,46 IMoS parameters for a representative calculation is included in the Supporting Information. To enable statistics, 15 to 75 independent calculations were performed for each model. PA and EHSS method calculations were performed using EHSS/ 2k.47 B

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and the bars that span from 10% and 90% of the cumulative distribution function.26 Ω̃Exp values for Ub1 ions from denaturing conditions range from 9.85 to 19.7 nm2 for z = 5+ to 13+. Ω̃Exp values for Ub1 ions from supercharging conditions range from 15.3 to 23.6 nm2 for z = 7+ to 20+. The Ω̃Exp values for the latter are systematically higher than the former. Interestingly, the latter span a narrower range of Ωvalues even though they span a greater range of z. For comparison, the ΩExp values reported39 for Ub1 ions generated from aqueous 200 mM ammonium acetate at pH 7 ranged from 9.72 to 10 nm2 from z = 4+ to 6+ (Figure 1B). Ω̃Exp values for Ub2 ions from denaturing conditions range from 17.9 to 39.9 nm2 for z = 9+ to 25+, and those from supercharging conditions range from 34.0 to 41.8 nm2 for z = 18+ to 28+. Only three additional charge states were detected under supercharging conditions relative to denaturing conditions, whereas supercharging yielded seven additional charge states for Ub1. Interestingly, the maximum Ω̃Exp for supercharged Ub2 was measured for the 27+ ion, and not the highest charge state measured, 28+, which had a Ω̃ of 41.2 nm2. For comparison, the ΩExp values for Ub2 ions generated under native-like conditions range from 15.6 to 17.9 nm2 and are shown in Figure 1B. ΩExp values for Ub1 and Ub2 ions from all three solution conditions depend on z. That dependence is greatest for intermediate charge states from denaturing and supercharging conditions, and is weaker for low-z native-like ions and the highest-z supercharged ions. The observed change in Ω with respect to z may have contributions from (1) differences in structure for ions of different z and/or (2) enhanced long-range interactions between the protein ion and He gas with increasing z. Decoupling these contributions is important for increasing the information content of native IM-MS experiments, which seek to probe the structures of ions in the gas phase in order to infer the structures of biomolecules in solution. Here, we investigate the contributions of ion-induced dipole interactions to the Ω-values of protein ions using the TJ method, seven methods for assigning the charge distribution, and four structural models. Effects of Charge Distribution on ΩTJ. We first considered a native model of Ub1, which was constructed as described in Methods and is shown in Figure S1A, and charge states ranging from 1+ to 22+, which spans from lowest-z ions generated using ion/ion proton transfer reactions24,49 to the highest-z ions generated using supercharging (Figure 1A). The net charge was assigned to the model using one of six methods, which are summarized in Table 1 and described further in the Supporting Information. These methods were selected to span a wide range of possible charge distributions, i.e., the degree and heterogeneity of the localized charges, and in turn the sensitivity of the resulting Ω-values to the selection of a specific method for distributing the charge. Ω-values were calculated using the TJ method and are reported in Figure 2A. For comparison, Ω-values calculated using the PA and EHSS methods are reported in Table S1 and are plotted with the ΩTJ values in Figure S2A. Overall, the ΩTJ values calculated using each charge distribution method increase with z, which is attributed to the increased ion-induced dipole interactions between the protein ion and the He atom during trajectories. The CoM and Even methods yield Ω-values that are smaller than those determined using the other charge distribution methods. The CoM method assigns the net charge to a single point, whereas the Even method distributes the net charge

Table 1. Description of Charge Distribution Methods method CoM CoD Even FF-Even FF-Protonation FF-Shuffle Random

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description Net charged placed at the center of mass of the protein. The partial charge of each atom is zero. Mass-proportional fraction of net charge placed at the center of mass of each domain. The partial charge of each atom is zero. All atoms are assigned an equal fraction of the net charge. Atoms are assigned a partial charge using Amber force field plus an equal fraction of remaining net charge. Atoms are assigned a charge using Amber force field; the net charge is then increased by increasing the partial charge of the most negative atom by one e. The charge distribution from FF-Even method is randomly reassigned to new atoms. Atoms are assigned a random charge from a normal distribution with the same mean and standard deviation as that generated using the FF-Even method.

RESULTS AND DISCUSSION Ions of many proteins exhibit increasing Ω-values with increasing charge state.23,24,29,48 For example, Figure 1A

Figure 1. (A) Ω-values as a function of charge state for Ub1 (blue circles) and Ub2 (red squares) from denaturing (solid) and supercharging (hollow markers) conditions. Vertical bars span the width of the apparent Ω-distribution (10% and 90% of the corresponding cumulative distribution function), and the markers indicate the median (Ω̃Exp) value.26 (B) ΩExp of Ub139 and Ub2 ions from native-like conditions. Horizontal dashed black lines correspond to ΩEHSS values calculated for the native models of Ub1 (11.15 nm2) and Ub2 (19.08 nm2, Table S2). Note that all experimental and calculated Ω-values in this study are for protein ions with He gas.

shows critical values from the experimental Ω-distributions of Ub1 and Ub2 ions generated from denaturing and supercharging conditions, as a function of charge state. Note that all experimental and calculated Ω-values in this study are for protein ions with He gas. The critical values are reported using markers that represent the median experimental Ω (Ω̃Exp, 50% of the cumulative distribution function of the Ω-distribution) C

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using these charge distribution methods are discussed later in this section. Results for the native model of Ub2 calculated using the CoM, Even, FF-Even, and FF-Protonation methods are shown in Figure S3A. Similar to the results for Ub1, the Ω-values determined using the FF-Even and FF-Protonation methods are similar to each other and greater than those determined using the Even method. The ΩTJ values for Ub2 calculated using these three methods increase with z, consistent with calculations using all six methods for Ub1, but ΩTJ values for Ub2 calculated using the CoM method decrease with increasing z. This surprising result will be discussed below. The differences between the ΩTJ values calculated using the six methods for assigning charge distributions must be due to differences in the electric fields that individual He atoms experience during trajectories, which affect the relative strength of ion-induced dipole interactions between the He atom and the protein ion and the momentum transferred during the trajectory. To help visualize the long-range interactions, Figure 3A shows potentials between a He atom and the native model of Ub1, using the Even method and eq 1, along an arbitrary axis that passes through the center of mass of the protein. These potentials for the zero-charge protein (this is the sum of the Lennard-Jones interactions) and 5+ ion are very similar, but those for the higher-charge protein ions exhibit both deeper wells and significant attraction at increasingly long distances. To extend this analysis, the potential was calculated on a plane that includes the preceding axis, using both the Even and FFEven methods. In the case of Ub1 with a net charge of zero, the attractive regions of the plane using the Even model (Figure 3B) exhibit smaller magnitudes and extend shorter distances from the protein than those found using the FF-Even method (Figure 3D). The attractive regions of the planes calculated for Ub1 with a net charge of 20+ (Figure 3C,E) are far more significant than those calculated using a net charge of zero. Furthermore, the potentials in the regions surrounding the protein calculated using the FF-Even method are less uniform than those calculated using the Even method. These differences are likely the origin of the systematic differences between the ΩTJ values calculated for this model using these two methods for assigning partial charges (Figure 2A). ΩTJ values calculated using the FF-Shuffle method are larger than those calculated using the FF-Even method, even though both methods use identical sets of partial charges that are assigned to different atoms (Table 1). To illustrate the differences in the electrostatic potentials on the surface of the ions, Coulombic surfaces of 1+ Ub1 using the FF-Even and FFShuffle methods were calculated as described in Methods. The Coulombic surface calculated for a model of 1+ Ub1 generated using the FF-Shuffle method exhibits larger magnitudes than that using the FF-Even method (Figure S4), which is attributed to the increased likelihood of partial charges with the same polarity clustering proximal to each other with random assignment. These Coulombic “hot spots” will induce greater dipoles in an approaching helium atom and consequently result in greater average momentum transfer and larger ΩTJ values. The finding of decreasing ΩTJ values with increasing z for the native model of Ub2 using the CoM method illustrates a significant limitation of using a single point charge to account for the net charge of a protein ion. The center of mass of this model is located in between the two domains in a region that is not occupied by atoms. For comparison, assigning a massproportional fraction of the net charge to the center of mass of

Figure 2. (A) ΩTJ values calculated using the native model of Ub1 (Figure S1A) and six charge distribution methods (Table 1) as a function of charge state. (B) Values calculated using the energy-relaxed model of Ub1. In each panel, the ratio of ΩTJ to ⟨ΩExp⟩ for Ub1 from native-like conditions (Figure 1B) is shown on the right-hand axis, where ⟨ΩExp⟩ is the mean of the ΩExp values for all charge states of native-like ubiquitin.39 The ΩEHSS value is plotted as a black horizontal line (Table S1). Vertical bars span the 95% confidence interval, based on independent calculations and t statistics.

evenly to all atoms. Despite distributing the net charge very differently, the Ω-values determined using these two methods are remarkably similar, e.g., 11.0 ± 0.1 nm2 for the 1+ ion and 12.4 ± 0.1 (CoM) and 12.3 ± 0.2 (Even) nm2 for the 22+ ion. The FF-Even and FF-Protonation methods yield ΩTJ values that are greater than those calculated using the CoM and Even methods. For net charges ranging from 1+ to 22+, the FF-Even method yielded values ranging from 11.3 ± 0.1 to 12.7 ± 0.2 nm2, respectively, whereas the FF-Protonation method yielded values ranging from 11.2 ± 0.04 to 12.7 ± 0.07 nm2, respectively. The FF-Shuffle and Random methods ΩTJ values are systematically larger than those determined using the other methods. For net charges ranging from 1+ to 22+, the FFShuffle method yielded values ranging from 12.3 ± 0.03 to 13.8 ± 0.05 nm2, respectively, whereas the Random method yielded values ranging from 12.3 ± 0.04 to 13.8 ± 0.05 nm2, respectively. The FF-Shuffle method yielded ΩTJ values that are about 1 nm2 greater than the FF-Even for each z, despite the two methods using identical sets of partial charges. Factors contributing to the differences in the Ω-values determined D

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from 1:1 water−methanol solutions all exhibited evidence for compact structures with Ω-values around 10 nm2.23 This difference is consistent with the structure of the protein evolving from that in solution to that probed in these gas phase experiments.52−54 Wyttenbach and Bowers reported that energy minimization of an NMR-derived structure of ubiquitin resulted in a “10% reduction in [ΩEHSS]...however, the secondary and tertiary structure is retained”.23 We found a similar result in terms of the change in Ω and the retention of higher-order structure upon energy relaxation of the native model; ΩEHSS values are reported in Table S1 and images of the model before and after energy relaxation are shown in Figure S1A,B, respectively. Figure 2B shows the ΩTJ values calculated from the energyrelaxed model of Ub1; this data is also shown relative to ΩPA in Figure S2C. The ΩTJ values for the low-z ions determined using the CoM, Even, FF-Even, and FF-Protonation methods are all similar to the values reported for the corresponding native-like ions.23,39 These values are also similar to the ΩEHSS values, which suggests that the ion-induced dipole interactions do not contribute significantly to ΩTJ values for these low-z ions. Interestingly, the ΩTJ values calculated using the CoM, Even, FF-Even, and FF-Protonated methods for the energy-relaxed model are more similar to each other than that similarity for the native model. This is attributed to increased charge solvation resulting from the energy relaxation. The increased charge solvation, which positions charges of opposite polarity in closer proximity, can be visualized from the differences in the Coulombic surfaces of the native and energy-relaxed models calculated using the FF-Even method (Figure 4). The surface for the energy-relaxed model exhibits significantly lower magnitudes than that for the native model, which would decrease the polarization of an interacting He atom. The FFShuffle and Random methods still yield larger ΩTJ values than the other methods after energy relaxation, because charge solvation is lost following the randomization.

Figure 3. (A) Interaction potential between a helium atom and the native model of ubiquitin, calculated along an arbitrary axis (x) whose origin is the center of mass of the model and as a function of charge state, which was distributed using the Even method. The potential was then calculated on a plane that includes x. The partial charge on each atom was assigned (B) a value of zero, (C) using the Even method with a net charge of +20, (D) using the FF-Even method with a net charge of zero, and (E) using the FF-Even method with a net charge of +20. For context, the repulsive regions of the potential are colored black and the xy position of each atom within 3 Å of the xy plane is plotted using a hollow circle.

each domain (CoD method) yields Ω-values that exhibit a dependence on z that is similar to those for the other methods (Figure S3A). These results provide insight into how the speed of future implementations of the TJ method may be increased by decomposing structures into structural domains,50,51 and placing charges proportional to the mass of each domain at each center. This approach would only require evaluation of a small number of ion-induced dipole terms, which will reduce the computational cost relative to the standard approach of placing a partial charge on each atom. Effects of Ion Structure. The ΩEHSS and ΩTJ values calculated for the native model of Ub1 are larger (≥10.7 nm2) than reported from many IM-MS experiments. For comparison, Ub1 cations generated from aqueous 200 mM ammonium acetate at pH 7.0 yielded 4+ to 6+ ions that had Ω-values of 9.7, 9.8, and 10 nm2,39 and z = ±6, ±7, and ±8 Ub1 ions generated

Figure 4. Coulombic surfaces of the native (A,B) and energy-relaxed (C,D) models of 1+ Ub1 with partial charges assigned using the FFEven method. E

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The Journal of Physical Chemistry A Relaxing the energy of Ub2 decreases the distance between the two domains (Figure S1E−H). ΩTJ values for energyrelaxed Ub2 using the CoM, CoD, Even, FF-even, and FFProtonation methods are shown in Figure S3C. Similar to Ub1, the average of the ΩExp values are more similar to the ΩTJ and ΩEHSS values for the energy-relaxed model than those values for the native model. The ΩTJ values calculated using all charge distribution methods are similar, including both the CoM and CoD methods, over all z. The ΩTJ values increase with z, indicating that ion-induced dipole interactions becomes significant at high charge states. Figure S2D shows the ratio of the ΩTJ values for each z to that for the corresponding 1+ ion, for energy-relaxed Ub1 and each charge distribution method. Despite the differences in the magnitude of the ΩTJ values (Figure S2C), the ratios for a given z are all similar and increase from one to approximately 1.10 to 1.12 from 1+ to 22+. This indicates that all of the methods for assigning the charge distribution to energy-relaxed Ub1 capture the increases in ΩTJ with increasing z. Figure S3D shows the analogous plot for Ub2. From 1+ to 29+ Ub2, the ratio increases from 1 to ∼1.10. The ratios for z ≤ 10 for Ub1 and Ub2, which includes all native-like charge states of these ions, are all close to one. This indicates that the effects of modest values of z on the ΩTJ values for the energy-relaxed models are small and that the net charge of these ions do not significantly affect the experimental Ω-values. IM-MS is widely applied to characterizing the structures of larger proteins and protein complexes. To extend the analysis to larger analytes, we selected alcohol dehydrogenase (ADH), a 147 kDa homotetramer. IM-MS experiments have been used to characterize ADH from native-like28 and supercharging55 conditions. ADH has also been used as a model system for characterizing the effects of charge reduction on the Ω-values of native-like ions.27,28,56,57 Those studies27,28,55−57 reported Ωvalues for 11+ to 37+ ions of ADH. Native (Figure S1I) and energy-relaxed (Figure S1L) models of ADH were built and the charge distribution was assigned using the FF-even method. Like the models of Ub1 and Ub2, ADH also compacts during energy relaxation. ΩTJ values were calculated as a function of z and are plotted in Figure S5. Unlike Ub1 and Ub2, whose ΩTJ values depend on z within the range of experimentally measured z, the ΩTJ of ADH depends weakly on z over the entire range of experimentally measured z, i.e., 11+ to 37+. There is not a clear trend between z and Ω for those charge states (Figure S5B,D) and all ΩTJ values over this range of z agree are similar to the corresponding ΩEHSS values. This indicates that differences in ion-induced dipole interactions have a neglible effect on ΩTJ over this range of z. ΩTJ values are greater than the ΩEHSS value at very high z, i.e., z > 70, which is much higher than observed experimentally for the tetramer of ADH. For comparison, the ratios of the ΩTJ values to the average of the experimental Ωvalues28 (⟨ΩExp⟩) are shown on the right-hand axis of Figure S5A,C. The ratios for z ≤ 40 show that calculations using the energy-relaxed model agree better with ⟨ΩExp⟩ than calculations using the native model, but that the calculated values are still systematically larger than ⟨ΩExp⟩. To summarize the effects of charge on ΩTJ values for the energy-relaxed models of Ub1, Ub2, and ADH, Figure 5 plots the ratio of the ΩTJ value for each z to that for the corresponding 1+ ion, as a function of the m/z of the ion. For Ub1 and Ub2, ΩTJ values appear to be independent of charge state for ions with m/z greater than ∼1100. ΩTJ then

Figure 5. Ratio of the ΩTJ value for a given charge to that for the corresponding 1+ ion as a function of m/z for the energy-relaxed Ub1 (blue), Ub2 (red), and ADH (black) using the FF-Even method. Ratios determined using alternative models and charge distribution methods for energy-relaxed Ub1, Ub2, and ADH are shown in Figures S2, S3, and S5, respectively.

increases rapidly with decreasing m/z. For ADH, ΩTJ values increase rapidly with decreasing m/z for m/z less than ∼3000. To help interpret the origin of these trends, Figure S6 plots the charge per unit radius, surface area, and volume expected for the sphere with the same average projected area as ⟨ΩExp⟩ for Ub1, Ub2, and ADH. The trends in Figure 5 are best correlated with the trends expected for charge per unit radius (Figure S6A). Comparisons between Figures 5 and S6A suggests that ion-induced dipole interactions become significant when z per unit radius exceeds ∼5 nm−1. In general, these results show that ion-induced dipole interactions between helium and native-like ions of globular proteins have a small effect on Ω-values over the range of z generated in typical native mass spectrometry experiments, e.g., using aqueous 200 mM ammonium acetate. The native and energy-relaxed models have many intramolecular interactions, which in turn increase the solvation of the individual point charges and reduce the contributions from ion induced-dipole interactions in the TJ method calculations. Consequently, ΩEHSS values, which do not explicitly treat charge, appear to be reasonably accurate for these ions. ΩEHSS values calculated for the native models are systematically larger than the corresponding ΩExp values but when the energy of those models are relaxed using a steepest-descent approach, ΩEHSS values for the resulting models are much closer to the corresponding ΩExp values. However, even after energy relaxation, ΩTJ values for Ub2 and ADH are still ∼5% larger than the corresponding experimental Ω-values. Consequently, future work will focus on the model generation process. Origin of Increase in Ω at High z. The highest charge state ions generated using supercharging of Ub1 and Ub2 have Ω-values that are more than twice as large as those for the corresponding native-like ions (Figure 1). Over this range of z, ΩTJ values calculated for the energy-relaxed models of Ub1 and Ub2 increase by only ∼10% (Figures S2D and S3D). Therefore, the large Ω-values observed for Ub1 and Ub2 with increasing charge must include contributions from more extended structures. To evaluate the contributions of ion-induced dipole interactions to the Ω-values of extended structures of Ub1 and F

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The Journal of Physical Chemistry A Ub2, we constructed α-helical and linear models of these proteins. Figure S2E,G shows ΩTJ values calculated for the α-helical and linear models of Ub1, respectively, using six methods for assigning charge distributions. Generally, the ΩTJ values increase with increasing charge from 1+ to 22+, except values for the linear model using the CoM method decrease for the high charges. Similar to results for the compact structures discussed previously, values calculated using the FF-Shuffle and Random methods are systematically higher than those calculated using the other methods, which is attributed to the closer proximity of similar polarity charges in random distributions. The trends with increasing charge calculated using the CoM method for these extended structures are different than those found using the other methods. This indicates the CoM method does not adequately capture contributions from ion-induced dipole interactions for less compact structures. Analogous results for Ub2 are shown in Figures S3E,G, except calculations using the FF-Shuffle and Random methods were not performed. In general, the trends for Ub2 are similar to those discussed above for Ub1. Relative to results for the compact models, the ΩTJ values for the extended structures depend more strongly on the charge distribution method. Figure S2F,H shows the ratio of the ΩTJ value for a given charge state to that for the corresponding 1+ ion, for the αhelical and linear models of Ub1, respectively; analogous results for Ub2 are shown in Figure S3F−H. This discussion will exclude calculations using the CoM method, which yielded anomalous results for the extended structures as discussed above. With increasing charge from 1+ to 22+, the ratios for the α-helical and linear models of Ub1 increase from 1.00 to 1.01 to 1.06, depending on the structural model and the method used to assign the charge distributions. These increases are significantly smaller than the increases of ∼1.10 and ∼1.15 found for the native and energy-relaxed models (Figure S2B,D), respectively. Because the charges in the extended structures are distributed over greater distances than those in the native and energy-relaxed models, the relative contributions of increasing z are less, but the selection of the charge distribution method has a greater effect. Figure 6A shows the ΩTJ values for all models of Ub1 using the FF-Even method, as well as the ΩExp values for comparison. As previously discussed, the magnitude of the ΩTJ values determined using the different methods increase in the following order: energy-relaxed model, native model, α-helical model, and linear model. To quantify the changes in Ω with increasing z, Figure 6B shows the Ω for a given charge state relative to the Ω for the corresponding 20+ ion, based on both experiments characterizing supercharged Ub1 and calculations using the linear model and the FF-Even method. The ratios are very different for z = 7+ to 16+, consistent with different structures for ions with different charge states in the experiments. However, from z ≈ 17+ to 20+ the ratios are similar. Therefore, for the highest-z ions observed experimentally it appears that increased ion-induced dipole interactions alone can account for the small increases in Ωvalues observed experimentally (without any additional changes in structure). Analogous comparisons for Ub2 are shown in Figure S7; it is not clear whether those conditions have been reached for Ub2.

Figure 6. (A) Experimental Ω-values for Ub1 generated from denaturing (solid blue), supercharging (hollow blue), and native-like (black) conditions, as a function of charge state. ΩTJ values calculated using the FF-Even method for all structural models are also shown (red triangles). (B) For linear Ub1 (red triangles, Figure S2G) using the FF-Even method, and supercharged Ub1 (hollow blue, Figure 1A), the ratio of the Ω value for a given charge state to that for the corresponding 20+ ion. (C) Expansion for 15 ≤ z ≤ 22.

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CONCLUSIONS The effects of charge state and charge distribution on the Ωvalues of protein ions were characterized using a combination of IM-MS experiments and TJ method calculations. Ub1 and Ub2 ions generated from different solution conditions exhibit more than a 2-fold increase in Ω with increasing charge state (Figure 1). Assuming either native or energy-relaxed structures, TJ method calculations exhibit less than a 1% increase in Ω with increasing charge state for ions with m/z values greater than 1100 (Figure 5). For m/z values less than 1100, those calculations exhibit a 10% to 15% increase Ω with increasing charge state over the range of charge states observed experimentally (Figures S2B,D and S3B,D). These increases are attributed to increased contributions from ion-induced dipole interactions, which increase both the maximum depth and the range of the attractive potential between the protein ion and a helium atom (Figure 3). For comparison, analogous G

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tials,59 are still recommended for smaller ions that are amenable to electronic structure calculations.33 Representing the charge of a protein ion using a single point charge (CoM method, e.g., Figure S2C) or a point charge for domain (CoD method, e.g., Figure S2C) was promising in some cases but yielded unreasonable results in others (e.g., results using the CoM method in Figure S3A,E,G). With further validation, approaches such as CoD method that only require the evaluation of a small number of ion-induced dipole terms may enable reduced-cost TJ method calculations with accuracy comparable to the standard approach of placing a partial charge on each atom.

calculations for the energy-relaxed model of ADH exhibit less than a 1% increase in Ω with increasing charge state for ions with m/z values greater than ∼4000, which is similar to that of the highest charge state observed from native supercharging conditions,55 and a 14% increase required the addition of 150 excess charges (Figure 5). Note that contributions from longrange interactions to the Ω of a protein ion with N2 will be more significant due to the greater polarizability of an N2 molecule than a He atom. This phenomenon is currently under investigation. Contributions from enhanced ion-induced dipole interactions with increasing charge state without additional structural changes can account for only a fraction of the increase in Ω observed experimentally. Linear and α-helical models of Ub1 and Ub2 yield larger ΩTJ values that are closer in magnitude to those observed experimentally for the highest charge states of those ions (Figures 6A and S3). However, those calculations exhibit smaller increases in Ω with increasing charge state (Figures S2F,H and S3F,H), which is attributed to distribution of the excess charge over greater distances. Ω-values determined from TJ method calculations depend to varying extents on the method used to distribute the charge of the ion (Table 1). For the native model of Ub1, ΩTJ values determined using the FF-Shuffle and Random methods are systematically larger than those determined using the FFProtonation and FF-Even methods, which in turn are systematically larger than those determined using the CoM and Even methods (Figure 2A). These trends are attributed primarily to relative propensity of these method to generate Coulombic “hot spots”, which can be visualized using slices of the potential (Figure 3 panel B to panel E) and Coulombic surfaces (Figures 4 and S4). Although there are significant differences in the absolute magnitudes of the ΩTJ values determined using the different methods, the relative increases with increasing charge state are all similar (Figure S2). For the energy-relaxed model of Ub1, the ΩTJ values determined using the FF-Protonation, FF-Even, CoM, and Even methods are more similar to each other (Figure 2B) than the similarity for the native model of Ub1 (Figure 2A). During energy relaxation, the magnitude of Coulombic “hot spots” when using the FFEven or FF-Protonation methods decrease (Figure S4), which decreases the relative contributions of ion-induced dipolole interactions between the protein ion and helium atoms. For ions with low charge states and folded structures, such as those formed in most native mass spectrometry experiments, Ω-values determined using the TJ and EHSS methods can be remarkably similar to each other. This finding is significant because the EHSS method is far cheaper47 than the TJ method. For ions with higher charge states, contributions from ioninduced dipole interactions between the protein ion and helium atoms become increasingly significant. This trend necessitates the use of the TJ method, particularly for the characterization of subtle differences in Ω-values (Figure 6B). On the basis of comparisons between the results for the native and energyrelaxed models of Ub1 and Ub2 (Figures 2 and 4), we recommend distributing charge on models of protein ions using the Even method. Although distributing charge using methods that depend on properties developed for force fields is appealing, the resulting ΩTJ values can depend strongly on local interactions between adjacent atoms, which may not be accurately represented in the structural model. Although not evaluated here, the use of Merz−Singh−Kollman partial charges,58 which adequately reproduce electrostatic poten-

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ASSOCIATED CONTENT

S Supporting Information *

The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.jpca.7b08154. Methods for assigning charge distributions, parameters for trajectory method calculations, Table S1, and Figures S1−S7 (PDF)

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. ORCID

Matthew F. Bush: 0000-0003-3526-4973 Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS The authors thank Stephanie C. Heard (University of Utah) for acquiring the IM-MS data for Ub2 from native-like conditions. The authors thank Professor Carlos Larriba-Andaluz (Indiana University−Purdue University Indianapolis) for sharing the Ion Mobility Spectrometry Suite (IMoS) used for these calculations and useful discussion. Acknowledgment is made to Eli Lilly and Company (Young Investigator Award in Analytical Chemistry to M.F.B.) and the Donors of the American Chemical Society Petroleum Research Fund for support of this research.

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