Ion Mobility Measurements of Nondenatured 12–150 kDa Proteins and Protein Multimers by Tandem Differential Mobility Analysis–Mass Spectrometry (DMA-MS)


The mobilities of electrosprayed proteins and protein multimers with molecular weights ranging from 12.4 kDa (cytochrome C monomers) to 154 kDa (nonspecific concanavalin A hexamers) were measured in dry air by a planar differential mobility analyzer (DMA) coupled to a time-of-flight mass spectrometer (TOF-MS). The DMA determines true mobility at atmospheric pressure, without perturbing ion structure from that delivered by the electrospray. A nondenaturing aqueous 20 mM triethylammonium formate buffer yields compact ions with low charge states, moderating polarization effects on ion mobility. Conversion of mobilities into cross-sections involves a reduction factor ξ for the actual mobility relative to that associated with elastic specular collisions with smooth surfaces. ξ is known to be 1.36 in air from Millikan’s oil drop experiments. A similar enhancement effect ascribed to atomic-scale surface roughness has been found in numerical simulations. Adopting Millikan’s value ξ = 1.36 and assuming a spherical geometry yields a gas-phase protein density ρ p = 0.949 ± 0.053 g cm−3 for all our protein data. This is substantially higher than the 0.67 g cm−3 found in recent low-resolution DMA measurements of singly charged proteins. DMA-MS can distinguish nonspecific protein aggregates formed during the electrospray process from those formed preferentially in solution. The observed charge versus diameter relation is compatible with a protein charge reduction mechanism based on the evaporation of triethylammonium ions from electrosprayed drops.


Tandem ion mobility spectrometry–mass spectrometry (IMS-MS) is of great utility in the analysis of gas-phase protein ions [1]. The IMS-MS combination has recently been used for the identification of aggregates that are undetected by MS alone [2, 3], the observation of coulombic stretching of highly charged protein ions [4, 5], and to probe gas-phase protein ion structure [614]. Mobility measurements are particularly interesting in the case of high-mass protein ions generated by electrospray, which are capable of taking on different conformations in the gas phase. However, there are several unresolved issues in protein ion IMS-MS measurement. First, with the exception of the recent report of Bush et al. [15], high-mass protein ions have so far been analyzed only by IMS-MS systems relying on a nonlinear mobility scale [8, 1012]. True mobility measurements for protein ions in a wide molecular weight range are thus necessary as a comparison standard for nonlinear IMS measurements. Second, it is still unclear if the measured gas-phase protein structures correspond to liquid-phase structures, and thus whether mobility measurement can be used to infer structural clues about proteins in their native conformations [16]. Clearly, the shorter the time and the milder the transfer from solution to gas, the closer the two structures will be [17]. In the aforementioned studies, as well as in most previous protein IMS-MS work, IMS was performed on electrosprayed protein ions using either a linear drift tube [4] or a traveling wave (T-wave) nonlinear IMS [9], both of which perform mobility separation in time. While electrospray ionization is rather mild and proceeds very fast, most prior drift-tube and all T-wave studies have provided substantial activation to the ions prior to mobility determination, by either applying strong RF (radiofrequency) fields for ion transfer, focusing, trapping, and declustering collisions, or energetically injecting the ions from a vacuum into the drift tube. While such collisions and voltage differences are useful for increasing measured signal intensity and decreasing mass peak widths [18], they may give rise to structural changes in protein ions [4].

An alternative to transient mobility separation in time using linear drift tubes or T-wave spectrometers is steady mobility separation in space with a differential mobility analyzer (DMA). DMAs separate ions into fan-shaped trajectories by combining a flow field and an electric field [19, 20], and are commonly used in the study of atmospheric aerosols. DMA-based IMS-MS of protein ions has several advantages. DMAs measure true mobility, and the mobility variable (i.e., the voltage difference between DMA electrodes, is linearly proportional to inverse mobility, simplifying DMA calibration as compared to nonlinear T-wave IMS. Just as quadrupole mass spectrometers can isolate ions of a specific m/z, DMAs act as mobility filters, transmitting only a narrow range of electrical mobilities centered on a prescribed value. This allows for DMAs to be readily coupled as front-end devices to almost any mass spectrometer with an atmospheric pressure ion source, without any modification in the operation of the MS [21]. Recently, high-transmission parallel-plate DMAs have been constructed with resolving powers in excess of 50 [22, 23], which are well suited to DMA-MS integration. In tandem DMA-MS with a parallel-plate DMA, the DMA operates at atmospheric pressure, and, unlike most other IMS-MS instruments, it can be used to measure the mobility of electrosprayed ions immediately following the evaporation of electrospray drops, without the need to subject the ions to RF fields, declustering collisions, energetic injection stages, or even vacuum interfaces.

While many features of the DMA-MS combination make it suitable for the analysis of electrospray-generated protein ions, the fact that the DMA measurement is milder than other IMS approaches does not by itself guarantee that the ion structure analyzed in the DMA will coincide with the liquid-phase structure. In fact, low-resolution differential mobility analysis of electrosprayed proteins has produced some controversial results. In earlier, groundbreaking studies, Kaufman and colleagues [24] used a charge-reduced electrospray source [2527], a low-resolution DMA (a shortened version of the Knutson and Whitby DMA [28]), and a sensitive single-ion detector (the condensation nucleus counter, CNC [29]) to measure the mobility diameter (that of a sphere of the measured mobility) of singly charged globular proteins ranging from 5.7 to 669 kDa in molecular weight. The ratio of the theoretical protein mass over the volume of a sphere with the inferred mobility diameter gave an effective protein density of ∼0.89 g cm−3 (after correcting for a voltage bias [30] and for the effect of gas molecular diameter [19]). This density is reasonable for gas-phase proteins, assuming that some residual water molecules remain bound to protein ions as they transit through the DMA (operating with filtered air at ambient laboratory humidity), as is the case for proteins in crystals [31, 32] under moderately dry conditions. These observations suggest that the protein structures measured in the DMA are somewhat indicative of the protein liquid-phase structure, since the loss of this residual solvent typically takes place at the vacuum interface to the MS. Removal of this residual solvent is believed to launch a denaturation process within characteristic times discussed by Breuker and McLafferty [17]. Recently, however, several research groups [33, 34] have used an electrospray-DMA-CNC system with a different DMA [35] (commercially available as the macroIMS system from TSI Inc.) to measure protein mobility diameters, from which a density of 0.67 g cm−3 has been inferred. This density is approximately half the bulk protein density determined from crystal structures (∼1.35 g cm−3 excluding voids) and is unreasonably low, even for protein ions with residual solvent bound. Subsequent studies [36] have shown that proteins analyzed with macroIMS (based on the commercial DMA run by different research groups, as well as based on two other DMAs) yield diameters that vary by as much as 15%. Although the origin of this disagreement has not been addressed, it is clear from Figure 3 of [36] that the only DMA in the study specifically designed to achieve high resolution at nanometer sizes gave systematically the highest protein densities (in the range of 0.81 g cm−3, and exceptionally 0.90 g cm−3 for avidin). Our use here of a DMA of an even higher resolving power to obtain protein densities in the range of 0.95 g cm−3 (discussed in detail here) confirms the need to use such special DMAs for structure determination.

Because of both the potential advantages of the application of differential mobility analysis to measure electrosprayed proteins and the ambiguous results found previously with low-resolution DMAs, further examination of electrosprayed proteins with DMAs is appropriate. In the present study, we utilize a high-resolution parallel-plate DMA (DMA P4, SEADM, Boecillo, Spain) coupled to a quadrupole time-of-flight mass spectrometer (QSTAR XL, MDS Sciex, Toronto, Canada) to measure protein and protein multimer ions in the 12–150 kDa range generated by electrospraying protein solutions in aqueous 20 mM triethylammonium formate. Use of this nondenaturing buffer gives rise to multiply charged protein ions, but with reduced charge states as compared to the more commonly used aqueous ammonium acetate buffer [37]. With the DMA-MS, we are able to clearly determine protein ion mobilities (in dry air) and masses simultaneously, from which we infer their spherical-equivalent diameters and effective gas-phase densities. We compare our results to those in previous DMA studies as well as to ion diameters inferred from early and recent drift tube IMS-MS measurements in He [4, 13, 14, 38]. Additionally, we demonstrate that the DMA-MS combination can distinguish between protein multimer ions formed nonspecifically during the electrospray process and those formed naturally in solution. Finally, we use DMA-MS measurements to investigate the origin of multiply charged protein ions in electrospray ionization.

Experimental and Methods Section

Proteins and Electrospray Ionization

Bovine erythrocyte ubiquitin (U6253), bovine heart cytochrome C (C2037), bovine pancreas ribonuclease A (R6513), chicken egg white lysozyme (L6876), equine heart myoglobin (M1882), ovalbumin (A5503), bovine serum albumin (A8531), and jack bean concanavalin A (L7647) were all purchased from Sigma–Aldrich (St. Louis, MO, USA). Proteins were dissolved in 20 mM aqueous triethylammonium formate buffer and desalted using Nanosep centrifugal filtration devices (Pall Co.) with a filter cutoff molecular weight that was at least 3 times less than that of each protein. Following filtration, proteins were dissolved in aqueous 20 mM triethylammonium formate buffer at concentrations in the 20–50 μM range. Protein solutions were electrosprayed using an electrospray source similar to that described previously [23], but with a 360 μM outer diameter, a 40 μM inner diameter capillary, and an outer diameter tapered down to approximately 60 μM at the capillary outlet. Samples were driven through the capillary with a backing pressure of 0.1 bar. The electrospray source was operated in the cone jet mode (confirmed by visual observation of the electrospray with a microscope camera when the electrospray capillary was several centimeters from the DMA upper electrode), producing droplets with initial diameters of ∼150 nm [27]. With these protein concentrations and this droplet size, droplets containing zero, one, or multiple proteins were produced. Although drops underwent coulombic fission prior to complete evaporation, rough calculations show that both single and nonspecific multimeric protein ions were generated under these conditions [39].

Differential Mobility Analysis–Mass Spectrometry

The coupling of DMA P4 and the QSTAR MS has been described previously [23]. The key features of the DMA-MS for the measurement of electrosprayed proteins are illustrated in Figure 1. A 1.0 l min−1 flow of dry CO2 gas was sent into the electrospray ionization source chamber to help maintain a stable electrospray. Unlike in many cylindrical DMAs, however, this flow of CO2 did not enter the DMA. The DMA was operated with a high velocity sheath flow of dry air (applied blower voltage 4 V, recirculating mode, 31°C in the classification region), and a small counterflow of air (∼0.3 l min−1) at the sample inlet. The counterflow served to prevent entry of CO2 and uncharged vapors into the DMA, as well as to drive the evaporation of electrosprayed droplets prior to their entrance into the DMA. Complete drop evaporation was checked for by measuring DMA-MS spectra with the electrospray needle at various distances from the DMA inlet. Although increasing the distance between the electrospray outlet and DMA inlet decreased the overall signal intensity, it did not cause any shift in the measured mobilities, showing that all free solvent evaporated prior to ions entering the DMA. Therefore, the electrospray capillary was moved close to the DMA inlet (< 1 mm separation distance) to maximize the measured ion signal intensity in the MS and to measure protein ions as close to their point of origin as possible. For tandem mobility and mass measurements, the voltage in the DMA was stepped in increments of 10 V, usually in the 1000–3500 V range for each protein. Voltages in this range have corresponding electric fields below 3.5 × 105 V m−1, so mobilities are measured in the low field limit. At each DMA voltage, a complete mass spectrum was measured in the time-of-flight section of the QSTAR XL (up to an m/z ratio of 20,000). Complete mobility-mass spectra with adequate signal detection were collected for samples in less than 10 min, and sometimes in as little as 2 min.

Figure 1

Schematic of the electrospray source and parallel plate differential mobility analyzer

As the DMA is a linear ion mobility spectrometer, DMA calibration only requires determination of the DMA voltage (potential difference between in outer and inner electrodes; see Figure 1) needed to transmit a single standard ion of known mobility. Ude and Fernandez de la Mora [40] measured the mobilities of a series of positively charged cluster ions in air at 20°C produced by electrospraying tetra-alkylammonium salt solutions. Their measurement of 0.528 cm2 V−1 s−1 for the mobility of the cluster ion (THA+)3(Br)2 (THA+ = tetraheptylammonium+) was used here for calibration, and the DMA voltage V s required to transmit this ion was determined during each day in which the experiments were performed. Because DMA P4 was operated above room temperature while the standard mobility was determined at room temperature, the standard ion mobility was adjusted using the hard-sphere model for ion mobility to 0.538 cm2 V−1 s−1. As shown by Ku and Fernandez de la Mora [41], the hard-sphere model works reasonably well at this mobility, particularly when correcting for a small temperature difference. With the DMA mobility scale calibrated, the mobility of each measured ion was determined from the equation

$$ Z = \frac{{{Z_s}{V_s}}}{{{V_{DMA}}}}, $$

where Z is the mobility of an ion selected when V DMA is the applied voltage in the DMA, Z s is the mobility of the standard, and V s is the DMA voltage required to transmit the standard (i.e., the voltage that gives the highest signal).

Results and Discussion

Tandem Mass-Mobility Spectra and the Effects of Declustering Potentials

The ability to probe ion structure prior to declustering, essentially as produced by the electrospray, is a useful feature of DMA-MS. However, when employing declustering potentials between the DMA and the MS (for the purpose of increasing ion transmission and removing solvent adducts), the ions measured in the MS are not necessarily identical in mass and mobility to the ions selected by the DMA [18]. Figure 2a shows a false color scheme contour plot of ion signal intensities from concanavalin A (conA) as a function of both m/z and the declustering potential (DP1, the potential difference between the orifice plate and the skimmer) in the MS. For these measurements, the DMA was set to transmit ions with an inverse mobility of 1.75 V s cm−2. The number of protein molecules per ion and ion charge state are labeled on the plot. Figure 2a shows that high declustering potentials substantially increase the signal due to two beneficial effects. One is that the removal of clusters sharpens peaks in the m/z dimension. The other is that an increased declustering potential also favors ion transmission. Several multimeric ions, the trimer+12 and tetramer+15, are only barely detectable at DP = 0, but become quite strong at higher DP. Others, such as the dimer+11, the monomer+6, and monomer+7, are imperceptible at DP = 0, but we believe they are parent ions rather than the product of dissociation. ConA+6 and ConA+7 could conceivably be fragments of the dominant dimer ions with z = 9 and 10 (ConA +92 , ConA +102 ), but this is unlikely for ConA+6 because it is already present at DP = 60 V. This is confirmed by the fact that ConA+6 has a mobility congruent with that of the more abundant dimer ions appearing clearly at DP = 0. ConA+7 will later be seen to also have the right mobility with respect to ConA+6 (Figure 3, discussed subsequently). Therefore, if ConA+6 is not a fragment, then ConA+7 cannot be a fragment either. ConA +112 cannot in turn be a fragment of either of these two dominant parents. There is accordingly no indication suggesting any dissociation of multimeric concanavalin A ions at any declustering potential, even though all product ions would necessarily remain at the selected mobility. We have subsequently carried out numerous additional measurements with concanavalin A and we can confirm its lack of tendency to fragment within the 0–250 declustering voltage range (Borrajo, R., Zurita, M., Fernandez de la Mora, J.: Relation between crystal structures and electrosprayed gas phase structure of concanavalin A, to be submitted to Anal. Chem.). Figure 2b shows raw DMA spectra at various declustering potentials for the lysozyme dimer (Lys2) with m/z corresponding to z = +7. The tallest peak seen at the highest voltage is indeed associated with (Lys2)+7. The second peak seen at ∼2100 V corresponds to the dimer that goes through the DMA as (Lys2)+8 but loses one charge between the DMA and the TOF region of the MS. A third peak is visible at ∼1900 V, which likely corresponds to (Lys2)+9 that loses two charges in the DMA-MS interface. As the declustering potential is decreased from 350 V to 50 V, the signal intensity ratio of +7 dimer ions to +8 dimer ions that have undergone charge loss increases from 1.44 to 2.92, showing that the declustering potential does indeed enhance charge loss. Also shown in Figure 2b is the narrower mobility peak for (THA+)3(Br)2, with FWHM ∼1.88%. Accordingly, the DMA has a resolving power in excess of 50, and the broader protein mobility peaks seen are due to either variable levels of adducts during mobility measurement, or to the coexistence of several gas-phase protein conformations.

Figure 3

False color scheme contour plots for protein ions. (a.) Cytochrome C (350 V declustering potential), (b) ubiquitin (350 V), (c) ribonuclease A (350 V), (d) lysozyme (250 V), (e) myoglobin (250 V), (f) ovalbumin (250 V), (g) bovine serum albumin (150 V), and (h) concanavalin A (350 V). Protein ion multimeric state and number of charges are labeled. White arrows denote ion peaks originating from charge loss between DMA and MS

Figure 3

False color scheme contour plots for protein ions. a. Cytochrome C (350 V declustering potential), b ubiquitin (350 V), c ribonuclease A (350 V), d lysozyme (250 V), e myoglobin (250 V), f ovalbumin (250 V), g bovine serum albumin (150 V), and h concanavalin A (350 V). Protein ion multimeric state and number of charges are labeled. White arrows denote ions peaks originating from charge loss between the DMA and MS

Representative false color scheme m/z versus mobility plots (with the most intense features depicted in red and the least intense in dark blue) are shown in Figures 2c and 3 for all measured proteins. Inverse mobility is used on the horizontal axis of Figure 3 because it is proportional to the ion cross-section over charge ratio (see Equation 2); thus larger and less charged ions appear in the upper right. The number of proteins per ion and the charge states are labeled in Figure 3 for the most prominent peaks. As the molecular weights of the monomers are known a priori, the charge and multimeric state of each detected ion could be directly determined. The data shown in Figure 3 were collected with moderate-to-high declustering potentials (250–350 V), as this was necessary to distinguish peaks corresponding to protein and protein multimer ions. Unfortunately, as mentioned above, declustering can lead to charge loss between the DMA and MS. This is further demonstrated by comparing Figure 2c (adapted from [42] for an especially clean lysozyme sample measured in CO2) and Figure 3d for lysozyme, taken with declustering potentials of 1 V and 250 V, respectively. The bare ions (lys n )+n in the series of n-mers should all have the same m/z. In reality, however, with only 1 V of declustering potential, their average mass increases with n, showing a level of clustering that increases with mass (monomer+5, dimer+10, trimer+15; dimer+12, trimer+18, etc.). In declustered lysozyme data, the excess adducts have been substantially removed prior to the mass measurement.

While it is possible that the presence of some peaks in the mass-mobility spectra could also be the result of the asymmetric dissociation of larger protein ions into monomers or lower order multimers between the DMA and MS, we find that this is an unlikely origin for the peaks observed here (with several possible exceptions to be discussed later). In the Electronic Supplementary Material (ESM), we provide complete mass spectra for selected proteins at various declustering potentials, and the mobility spectra (in terms of DMA voltage) for high m/z ions (m/z > 8,000) in each spectrum. All detected high m/z ions had inverse mobilities higher than the mobilities of peaks shown in Figure 3 (and hence were transmitted at higher DMA voltages); thus, if they fragmented between the DMA and MS, their products would appear at higher inverse mobilities than the peaks in Figure 3. Moreover, as shown later in this manuscript, the charge states of the observed ions appear to be reduced by the kinetics of ion evaporation of triethylammonium ions [43]. Such strong agreement between measured charge states and ion evaporation models would not be expected for the product of asymmetric dissociation [44]. We therefore conclude once more that charge loss, but not multimeric dissociation, is prevalent with increasing declustering potential.

Clearly, increased declustering complicates the DMA-MS spectra, with the appearance of product ion mass peaks at parent ion mobilities. Fortunately, charge loss is far more readily identifiable in DMA-MS than in more conventional MS or IMS-MS methods. Charge loss transitions are marked in Figure 3 with white arrows, which extend at a given mobility from the m/z with which the ion went through the DMA to the m/z with which it went through the MS. Typically, only a single charge is lost from ions between the DMA and MS, though in some instances multiple charge loss is observed (for example the lysozyme ions mentioned above). Other anomalous peaks merit discussion. A cytochrome C+3 (CytC+3) peak with an inverse mobility of 1.56 V s cm−2 is clearly identifiable as a monomer via direct assignment of z from the spacing between multiple sodium adducts. This ion has an unreasonably small mobility for its mass, and must be a fragment of CytC +72 , which appears at exactly the same mobility. This fragmentation mechanism, if it is in fact the origin of the CytC+3 peak, is not observed so clearly here for other protein multimer ions, but has been observed at a declustering voltage of 350 V for GroEL tetradecamers measured by DMA-MS [45]. A monomer ribonuclease A+3 peak with an inverse mobility of 1.41 V s cm−2 shows a similar anomaly, though its origin as a fragmentation product of a parent ion of the same mobility is not so clear-cut. The two monomer ions CytC+4 and a CytC+3 with inverse mobilities of 1.40 V s cm−2 both originate from CytC+5 (detected in separate experiments with an inverse mobility of 1.40 V s cm−2) through two successive charge loss events. All of these peaks are similarly identifiable as monomers from the spacing in m/z between successive sodium adducts.

The myoglobin spectrum is complicated by the presence of both holo- and apomyoglobin ions, particularly at higher multimeric states where various combinations of holo- and apomyoglobin ions are observed. Nonetheless, the charge and multimeric states are identifiable in the contour plot. The mobilities of the holo- and apomyoglobin ions are similar (except for the +5 holo- and apomyoglobin monomers), showing that for some myoglobin ions, the loss of heme occurs either during or shortly after electrospray drop evaporation, but prior to ions entering the DMA. The minimum FWHM obtainable approached 3% (for myoglobin ions), but was often substantially higher, particularly for ovalbumin and bovine serum albumin ions. This peak width supports the notion that larger protein ions gather a greater level of adducts, or exhibit a wider distribution of conformations. Some peaks are also broadened and slightly shifted by charge loss interference. Quite often, an ion composed of n protein monomers and z charges has a similar mobility to a protein ion composed of n + 1 protein molecules and [(n + 1)/n](z − 1) charges, causing overlap in the mobility spectrum if charge loss occurs between the DMA and MS (e.g., in the lysozyme spectrum of Figure 3d, the 1+5 to 1+4 transition leads to a peak that interferes with the 2+8 peak, and the 3+10 to 3+9 transition interferes with the 4+12 peak).

Protein Diameter and Density Versus Measured Mobility

In the absence of polarization effects, the hard-sphere limit can be used to describe the relationship between the mobility Z and the diameter d i of smooth spherical ions. For ions with diameters that are much smaller than the mean free path of the gas molecules, the free molecular limit applies, leading to:

$$ \frac{{\rm Z}}{{\sqrt {{1 + {m_g}/{m_i}}} }} = \frac{1}{\xi }\frac{{ze}}{{p{{\left( {{d_i} + {d_g}} \right)}^2}}}\sqrt {{\frac{{9{k_B}T}}{{8\pi {m_g}}}}} , $$

where m g is the mass of the gas molecule, m i is the ion mass, k B is Boltzmann’s constant (1.38 × 10−23 J K−1), T is the temperature in the DMA, z is the number of charges on the ion, e is the charge on the electron (1.6 x 10−19 C), p is the pressure in the DMA (atmospheric pressure), and d g is the diameter of the drift gas molecules (taken as 0.3 nm at room temperature, from previous measurements in air [41]). The coefficient ξ included in the denominator of the right-hand side of Equation 2a is unity for the ideal case of elastic and specular collisions. However, this is no longer true for real ions or particles. For these species, ξ > 1 is an empirical drag enhancement factor that decreases the mobility over its ideal (smooth, elastic, and specular) value. The need for this factor arose during Millikan’s determination of the electron charge, which relied on precise measurements of the velocity of oil drops in gases [46]. In the limit of small drops at reduced gas pressure, Millikan’s work showed that ξ = ξ M = 1.36, in other words the measured drag is 36% larger than expected for ideal hard spheres. While Millikan’s early studies did not include drops as small as most proteins, many subsequent investigations have confirmed the value ξ = 1.36 down to rather small dimensions in air [41, 47, 48]. Following Epstein [49], the drag enhancement factor has been written as

$$ \xi = \left( {1 + \pi {\alpha_{\rm{I}}}/8} \right), $$

and interpreted as due to the fact that a fraction α I (∼0.91) of the gas molecules interact inelastically with the ion. Although most studies on small clusters and proteins via IMS-MS have for a long time ignored Millikan’s drag enhancement factor (with some exceptions, e.g., [50]), the need for a coefficient ξ > 1 in (2a) was rediscovered 15 years ago through model calculations [51] applied to moderately small clusters such as fullerenes. In their simplest form, these calculations have relied on the so-called exact hard-sphere scattering model (EHSS), where each atom in the ion is treated as an individual hard sphere undergoing elastic and specular collisions with the gas. This approach showed drag coefficient enhancements that depend on geometry and ion size, and in some cases exceed ξ EHSS = 1.20 [52]. Calculations for symmetrically growing aggregates of fullerenes yielded an enhancement factor that decreases linearly with curvature and extrapolates at large sizes to 1.3 (Figure 3 of [51]):

$$ {x_{{\rm{EHSS}}}} - 1.3\sim - {m_{\rm{i}}}^{{ - 1/3}}. $$

Interestingly, Tammet [53] had previously advocated a smooth variation of ξ from ξ M for large particles down to unity for small molecules or atoms, though without providing the simple functional dependence (2c). The EHSS model has also been used for relatively complex ions, such as proteins [4], though even this simplification becomes increasingly untractable for increasingly large proteins [52]. Contrary to Epstein’s interpretation, the drag enhancement factor found in these model calculations has been ascribed to multiple scattering during elastic ion–molecule collisions, resulting from the atomic-scale roughness of the surfaces of essentially all large particles. It is interesting that a model where the gas molecules rebound elastically but diffusely (all directions of reflection being equiprobable) gives ξ = 4/3, very close to Millikan’s value. However, Epstein showed that this elastic-diffuse model was thermodynamically inconsistent, and therefore opted for an inelastic interpretation. What is apparent now though is that there are elastic mechanisms to explain Millikan’s findings, not only through multiple scattering, but also through the effective randomization of the reflection angle also forced by surface roughness.

There is still some discrepancy between extrapolations from theoretical calculations of ξ and measured values of it (a difference of 4.4%). It has been estimated by model calculations to be 1.3 in He, but has long been known from careful experiment to be 1.36 not only in air but several other studied gases, including He [5456]. The ambiguity in ξ is more significant in the case of clusters of moderate size. For these, EHSS calculations predict a size dependence that is approximately captured by Equation 2c, with ξ EHSS ∼ 1.2 for small proteins, and ξ close to unity for small clusters (both in He). In contrast, in air, we have confirmed Millikan’s value of 1.36 with ionic liquid cluster ions that are smaller than the smallest intact protein ions [41, 57]. Nonetheless, it follows both from model computations and from measurements with small drops that the drag on globular ions is increased, probably due to molecular-scale roughness rather than inelastic collisions. Furthermore, it is clear that the conversion of a measured mobility into a protein cross-section should not be based on the assumption ξ = 1, even though this approach has often been followed for small [2] as well as large [9, 12] peptide and protein ions.

Several authors, unaware of Millikan’s precedent, have advocated the use of the EHSS model for proteins [9, 52, 58]. We believe that Millikan’s 1.36 factor is more reliable not only for large but also for small proteins in air for three reasons. First, it has a firm experimental basis for globular shapes, covering all the relevant protein size range. Second, although the EHSS model has demonstrated great utility in the case of small clusters of reasonably well-known structure [5961], its empirical support is much weaker for proteins whose gas structure is not firmly known, and most often differs from the crystal structure (even for protein ions electrosprayed from neutral aqueous solutions) [4]. Finally, EHSS calculations become increasingly difficult at large protein masses, and would be even harder in molecular gases and with the largest ions used here. Our selection of ξ = 1.36 over the full protein size range is therefore the best available choice for interpreting our measurements in air.

A first test of the applicability of Equation (2a) with constant ξ = 1.36 can be made by noting that it predicts a linear relation between (z/Z)1/2 and protein diameter. Hence, for spherical proteins of fixed density (for which d i ∼ m i 1/3), a plot of (z/Z)1/2 as a function of m 1/3 should yield a straight line. This expectation is in fact observed to a first approximation in Figure 4a, even though there is a modest scatter for each multimer, which is particularly evident for the concanavalin A hexamers (the uppermost group of the data points). In general, a slight increase in (z/Z)1/2 is found with increasing charge state. This effect suggests that ion-dipole forces or coulombic stretching have a small effect on mobility, even with the use of a charge-reducing buffer. Unfortunately, the scatter in the data associated with the finite peak width precludes correcting for polarization (or other effects leading to a variation of cross-section with z), limiting the accuracy with which we may infer protein sizes from these data. This problem is still tolerable for our present purposes, and has been overcome in subsequent studies using a single protein (the GroEL tetradecamer) [45].

Figure 4

a (z/Z)1/2 as a function of m 1/3i . b Protein ion diameter as a function of ion mass. Black circles indicate this study. White squares are data from [24]. Gray triangles are data from [33] and [34]. The dashed line denotes the power law regression d i = 0.1438 m i 0.3369 (R 2 = 0.992)

To provide an accurate determination of the diameters of the largest protein ions, one must refine (2a) to account for slight continuum effects in the mobility. These effects are included in the Stokes–Millikan equation [41, 62]:

$$ {Z}{\left( {1 + \frac{{{m_{\rm{g}}}}}{{{m_{\rm{i}}}}}} \right)^{{ - 1/2}}} = \frac{{ze{C_{\rm{C}}}\left( {{d_{\rm{i}}} + {d_{\rm{g}}}} \right)}}{{3\pi \mu \left( {{d_{\rm{i}}} + {d_{\rm{g}}}} \right)}} $$
$$ {C_{\rm{C}}} = 1 + \frac{{2\lambda }}{{{d_{\rm{i}}} + {d_{\rm{g}}}}}[1.257 + 0.4{e^{{ - 0.55({d_{\rm{i}}} + {d_{\rm{g}}})/\lambda }}}], $$

where μ is the gas viscosity and λ is the mean free path of the gas molecules (66.5 nm at standard conditions). For each detected and identifiable ion, m/z and mobility are determined at the local maximum in signal intensity in contour plots, and Equation 3a is subsequently used to determine the ion diameter. Equation 3a converges to Equation 2 for d i << λ provided that ξ = 1.36. The protein analyzed, the m/z value, ion mobility, number of proteins per ion, ion diameter, and charge state are listed for selected ions in Table 1 and for all measured ions in the ESM. Protein ion diameters are shown as a function of ion mass (the product of m/z and z) in Figure 4b. Also shown are macroIMS data from Kaufman et al. [24, 30] (white squares) and those measured by Bacher et al. [33] and Kaddis et al. [34] (gray triangles) in a similar mass range. A power law regression to our data is also shown (d i = 0.1438 m i 0.3369; R 2 = 0.992), which has almost exactly the expected 1/3 power dependence. A best fit with a 1/3 power gives a slightly different constant of 0.1495, which, for spherical ions, reveals a bulk density of 0.949 g cm−3 ± 0.053 g cm−3. The charge-reduced electrospray-DMA-CNC measurements of Kaufman et al. [24] give a slightly smaller density of 0.893 g cm−3. This is to be expected, as their charge-reduced electrospray is designed to prevent secondary atomization via coulombic fission, significantly increasing the amount of adduct formation from impurities in the ES drops. Since the density is inferred from the measured protein size (with water and other adducts), but is based on the mass of the pure protein, this foreign matter always decreases the inferred density. The much lower density of 0.668 g cm−3 obtained by Bacher et al. [33] and Kaddis et al. [34] is paradoxical, as their work relies on the commercial version of exactly the same technique used by Kaufman et al. [24]. This anomaly and recent discrepancies in inferred protein diameters from different MacroIMS systems [36] have already been addressed in the “Introduction,” and suggest the need to base the measurement on DMAs that are capable of high resolution at nanometer sizes.

Table 1 Summary of selected protein ion measured m/z, mobility, protein molecules per ion, charge state, and inferred mobility diameter (diameter column)

Comparison of DMA-MS results to drift tube IMS-MS results is also of interest, as the two methods of analysis are capable of producing comparable data sets. Tables 2 and 3 summarize inferred diameters from mobility measurements for cytochrome C and lysozyme ions, respectively, from this study and prior studies [4, 13, 14, 38, 63]. For each measured ion we list the number of protein monomers per ion and the charge state. The “monomer ion diameter” columns refer to the inferred diameters of the monomer from mobility measurements (for the ions composed of n protein monomers, the value tabulated is that inferred for the whole ion divided by n 1/3). Because mobility measurements were made in this study prior to any declustering, and in prior studies the ions passed through regions of high declustering potential, we report both the mean monomer diameter and minimum monomer diameters for our measurement, inferred from the point of maximum signal intensity and the lowest detectable inverse mobility, respectively, for each ion peak in the spectra. We list two diameters inferred with the extreme assumptions ξ = 1.36 and ξ = 1. As already discussed, the expected value in He is greater than 1, and for sufficiently large ions it should approach 1.36 [54], so the differences between both columns capture the largest conceivable effect of ξ. In all calculations the diameter of the gas molecule is accounted for; it is taken as 0.3 nm for “air” molecules [40] and 0.2 nm for He molecules [64]. Finally, the study to which each data point corresponds [4, 13, 14, 38, 63] and the ionization technique used in the study are listed. All other studies used He as a drift gas, and the ionization technique in each study was different (note that we perform ESI under nondenaturing conditions, while strongly denaturing acidic solutions were used in other studies). The first thing to note is the large differences between the MALDI data and the ES data in He. Why MALDI gives rise to far more compact structures for both proteins is perplexing. For the MALDI data set, with ξ = 1.00 and approximating protein ions as being spherical, the average ion density comes to 1.22 g cm−3, close to the density of bulk peptides (not accounting for inevitable void spaces). However, with the more realistic values ξ = 1.20 and ξ = 1.3, the average inferred density takes unnaturally high values of 1.63 g cm−3 and 1.85 g cm−3, respectively. There is also a considerable difference in density between the monomer and multimer ions generated by MALDI, as is clear from the decrease in apparent monomer diameter for the multimer ions. The differences between the various measurements of ions in He are much smaller than those with the MALDI data (although there are still noticeable differences across experiments and across charge states), and in light of the unique results for MALDI-generated ions, we restrict comparisons of our data to measurements of non-MALDI-generated ions. For cytochrome C, the diameter in air (∼3.4 nm) is in-between the two extreme bounds for the He data (∼2.9 nm for ξ = 1.36 and 3.6 nm for ξ = 1.00). The inferred diameters from the measurements of Shelimov et al. [4] are brought into agreement with our measurements if ξ He = 1.1, which also narrows the gap between the other listed measurements and our own. This inferred ξ He is lower than the bounds predicted by EHSS calculation [51], suggesting that different ion structures were examined here and previously. Lysozyme measurements in air and He [63] give matching diameters when using ξ Ηe = 1.3. In general, if the same structures were measured here and in earlier IMS-MS work with cytochrome C and lysozyme, then the ξ in He is indeed bound between 1.1 and 1.3 for ions in this size range.

Table 2 Summary of inferred monomer diameters from IMS-MS studies of low-charge-state cytochrome C ions, taking ξ as 1.36 and 1.00. All other listed studies used He as a drift gas during measurement
Table 3 Summary of inferred monomer diameters from IMS-MS studies of low-charge-state lysozyme ions, taking ξ as 1.36 and 1.00. All other listed studies used He as a drift gas during measurement

However, the apparent random differences between earlier IMS-MS work and our experiments are substantial; thus, it is more likely that the variations observed across the board are due to the fact that different structures are being measured, as opposed to ambiguities in ξ. Very recently, Bush et al. [15] measured the mobilities of protein ions ranging from 12 to 801 kDa with a drift tube IMS-MS instrument, using both N2 and He buffer gas. Analysis of these newer data (not shown) with Equation 2a and ξ = 1.36 for both gases gives protein ion densities of 0.86 g cm−3 (regression R 2 > 0.99) and 0.93 g cm−3 (regression R 2 > 0.99) in N2 and He, respectively. These values are in excellent agreement with our inferred density of 0.949 g cm−3 and the density of 0.893 g cm−3 inferred from the work of Kaufman et al. [24]. The approximate convergence of these three studies on a protein ion density close to 0.9 g cm−3 suggests that ξ = 1.36 is valid not only in air and N2, but also in He for both large and small ions. Although these three studies relied on very different mobility analysis methods, the electrospray conditions employed were very similar (nondenaturing), further suggesting that there is some difference in the structures of ions produced from denaturing and nondenaturing solutions, which precludes clear comparison with earlier IMS-MS work.

Specific Versus Nonspecific Multimers

Many of the multimer ions examined in this study were produced nonspecifically during the electrospray process due to the unusually high protein concentrations used. When studying proteins that are less well characterized than those used here, the identification of specific multimeric states may be of interest [65]. It has been argued previously that for multimer ions originating nonspecifically during the electrospray process, the intensity distribution as a function of the degree of aggregation should follow a Poisson distribution [39, 66]. Regardless of the exact functional form of the multimer size distribution, nonspecific aggregates would follow a unimodal distribution. Figure 5 shows the size distributions of all protein ions examined, determined from maximum intensity values in contour plots. Charge loss between the DMA and the MS was accounted for in each measurement, but no corrections were made for differences in transmission efficiency for ions of different m/z. All size distributions are nearly unimodal, with the exception of that for concanavalin A, which is overly abundant in dimers and tetramers. Not surprisingly, concanavalin A tetramers form specifically in solution, confirming that DMA-MS can be used to identify specific solution-phase protein multimers.

Figure 5

Protein ion size distributions determined from peak intensities in contour plots with charge loss accounted for

Mechanism of Protein Electrospray Ionization

Although electrospray ionization has been a central tool for the analysis of macromolecules for almost 20 years, debate still persists regarding the origin of the number of charges per protein ion. Recently [67, 68], quantitative support has grown for the hypothesis that protein ions are formed as charge residues, but that their charge state is sometimes determined by the kinetics of ion evaporation [69] from electrospray drops (i.e., determined by the solvation energy of the buffer ions). DMA-MS measurements are ideal for further testing this hypothesis. From ion evaporation kinetic models [70, 71], a relationship between the ion size and ion charge state is expected when ions are formed as charge residues, which is given as [72]:

$$ {d_{\rm{i}}} = {d^{{*}}}F\left( {{z_{{\rm{mean}}}} - 1/2} \right) + {d^{{ *}}}\alpha $$

where z mean is the average charge on ions of diameter d i (correcting for charge loss in the DMA) and the function F(z mean − 1/2) is described and tabulated elsewhere [73]. Figure 6 shows protein ion diameter as a function of F(z mean − 1/2) for all data taken with triethylammonium formate buffer (black circles). Also shown are data points that use the mean charge states on protein ions determined by Hautreux et al. [75] (white squares) with triethylamine added to the electrospray buffer, as well as the data of Hogan et al. [67, 68] (gray triangles) with 10 mM triethylammonium bicarbonate buffer. Protein diameters for these two data sets were determined using the power law regression developed here. The dashed and dotted lines shown on the figure represent the d mean versus F(z mean − 1/2) relationship expected if the protein ions had charge states determined by the Rayleigh limit of water (Equation 4) and 50% the Rayleigh limit of water. Clearly, protein ions are not charged close to the Rayleigh limit. There is a reasonably good linear correlation (R 2 = 0.96) between d i and F(z mean − 1/2), suggesting that the charge on protein ions is determined by triethylammonium buffer ion evaporation from electrospray drops. The linear fit yields d * = 2.19 nm, α = 0.20, from which we infer an activation energy ΔG = 1.78 eV. Similarly, Castro [75] inferred ΔG = 1.73 eV for ion evaporation of triethylammonium ions. Note, however, that protein charge state from aqueous electrosprays appears to be determined by ion evaporation only when the solvation energy of ions is sufficiently low, such that ion evaporation occurs for droplets charged below the Rayleigh limit. Without the use of buffer salts with unusually low ΔG, ion evaporation around globular aqueous proteins will not occur. Furthermore, for ion evaporation to determine protein charge states, protein ions must form as charged residues (i.e., they themselves must not be formed by ion evaporation). For more highly charged proteins, often found when electrospraying denaturing solutions, there is evidence that protein ions are not formed as charge residues [42, 68, 76].

Figure 6

Protein ion diameter as a function of the ion evaporation parameter F(z mean − 1/2). Black circles indicate this study. White squares show data from Hatreux et al. [74]. Gray triangles show data from Hogan et al. [68]. Dashed line indicates the expected curve for the Rayleigh limit of water. Dotted line depicts the expected curve for 50% of the Rayleigh limit. Solid line shows the linear regression curve


We have used a newly developed parallel-plate DMA mounted on the front end of a QSTAR mass spectrometer to study electrosprays of protein and protein multimer ions to reach the following conclusions:

  1. 1.

    Mobilities (in air) have been obtained for proteins and protein aggregates electrosprayed from nondenaturing aqueous solutions. For the first time, the ions are as produced by the electrospray process. The data set covers a mass range up to 150 KDa.

  2. 2.

    While declustering is not implemented prior to mobility measurement in the DMA, a properly selected declustering potential at the entry of the MS permits sharp mass peaks to be obtained without substantial distortion to the original link between mobility and mass.

  3. 3.

    A broad critical examination of available information on the ratio ξ between the drag on real spheroidal ions and that on smooth ideal hard spheres has been undertaken for the first time. It reveals that the assumption ξ = 1 is never sound for proteins, and that ξ for large ions tends to 1.36, leaving little room for ambiguities in the case of large ions. For air there is compelling information indicating that the value ξ = 1.36 applies for proteins of all sizes. Model calculations in He suggest a size dependence of ξ with values perhaps as low as 1.2 for small proteins. In view of these facts, we interpret our own data at all protein sizes based on Millikan’s value ξ = 1.36.

  4. 4.

    Comparisons between existing data are difficult due to clear variations between different ion production methods, charge states and instruments.

  5. 5.

    The mobilities obtained for protein ions by DMA-MS imply relatively compact structures. When interpreted as corresponding to spheres with the known ion mass, a mean density of 0.949 g cm−3 results for all ions studied. This value is considerably larger than previously found with macroIMS for larger proteins.

  6. 6.

    DMA-MS measurements can be used to distinguish between nonspecific protein aggregates formed during the electrospray process and multimers forming specifically in solution.

  7. 7.

    Our measurements in aqueous triethylammonium formate are compatible with the notion that low-charge-state protein ions are charged residues whose charge state is determined by ion evaporation.


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We thank Alejandro Casado of SEADM and Bruce Thomson of MDS Sciex for the advice they gave during the setup of the DMA-MS system. We are grateful to Applied Biosystems and SEADM for the loan of the MS and the DMA, respectively, and to the Yale Keck Biotechnology Center for hosting the tandem instrument.

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Correspondence to Juan Fernández de la Mora.

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Submitted to: Journal of the American Society for Mass Spectrometry

Electronic supplementary material

Below is the link to the electronic supplementary material.

Supplementary Information

Complete mass spectra of selected proteins, mobility spectra of low- and high-mass ions, and a table listing the properties of all measured proteins ions (DOC 411 kb)

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Hogan, C.J., de la Mora, J.F. Ion Mobility Measurements of Nondenatured 12–150 kDa Proteins and Protein Multimers by Tandem Differential Mobility Analysis–Mass Spectrometry (DMA-MS). J. Am. Soc. Mass Spectrom. 22, 158–172 (2011).

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Key words

  • Ion mobility
  • Native-state protein MS
  • Differential mobility analysis
  • Charge reduction
  • Gas-phase protein conformation