On the Formation of Highly Charged Gaseous Ions from Unfolded

Jul 9, 2012 - The latter process commences with unraveling of a single subunit, in concert with Coulombically driven proton transfer. The subunit then...
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On the Formation of Highly Charged Gaseous Ions from Unfolded Proteins by Electrospray Ionization Lars Konermann,* Antony D. Rodriguez, and Jiangjiang Liu Department of Chemistry, Western University, London, Ontario, N6A 5B7 Canada S Supporting Information *

ABSTRACT: Electrospray ionization (ESI) of native proteins results in a narrow distribution of low protonation states. ESI for these folded species proceeds via the charged residue mechanism. In contrast, ESI of unfolded proteins yields a wide distribution of much higher charge states. The current work develops a model that can account for this effect. Recent molecular dynamics simulations revealed that ESI for unfolded polypeptide chains involves protein ejection from nanodroplets, representing a type of ion evaporation mechanism (IEM). We point out the analogies between this IEM, and the dissociation of gaseous protein complexes after collisional activation. The latter process commences with unraveling of a single subunit, in concert with Coulombically driven proton transfer. The subunit then separates from the residual complex as a highly charged ion. We propose that similar charge equilibration events accompany the IEM of unfolded proteins, thereby causing the formation of high ESI charge states. A bead chain model is used for examining how charge is partitioned as protein and droplet separate. It is shown that protein ejection from differently sized ESI droplets generates a range of protonation states. The predicted behavior agrees well with experimental data. +

P

zRH]zR , where zR is the Rayleigh charge of protein-sized water droplets (eq 1).1,5−7 Protein ESI charge state distributions (CSDs) show a dramatic dependence on the solution-phase structure.8,9 ESI of unfolded proteins produces very broad CSDs centered at values much higher than zR of the native state. Volatile acids are most commonly used for inducing solution-phase unfolding in ESI-MS, but the same CSD effects are observed after denaturation by base, organic cosolvents, heating, or disulfide cleavage,8−11 as well as for intrinsically disordered chains.12 Although a variety of factors can modulate the appearance of protein ESI mass spectra, it is undisputed that the solutionphase conformation represents the main determinant of the measured CSDs.13 Thus, ESI mass spectra provide a sensitive tool for monitoring protein folding/unfolding in solution.12−16 The CRM is well established for folded proteins,1,5−7 but it does not apply to unfolded species. As a result, a mechanistic understanding of the relationship between solution-phase conformation and ESI charge states is still lacking.3 Clearly, ESI charge states do not match those in bulk solution.13,17,18 Hence, it can be ruled out that changes in CSDs reflect the solution-phase titration behavior of ionizable groups.10 Here we develop an electrostatic model that accounts for the relationship between protein structure and CSDs. The model is validated through comparisons with experimental data.

roteins are among the most widely studied analytes in electrospray ionization (ESI) mass spectrometry (MS). ESI generates multiply protonated [M + zH]z+ gaseous ions from proteins in solution. The ESI process starts with highly charged micrometer-sized droplets that are emitted from a Taylor cone. In positive ion mode, much of the excess charge is due to protons produced by redox processes inside the ion source. Solvent evaporation increases the droplet charge close to the Rayleigh limit, where the number (zR) of elementary charges e is given by zR =

8π (ε0γrdroplet 3)1/2 (1)

e

with the radius rdroplet, the vacuum permittivity ε0, and the surface tension γ. When the charge approaches this critical value the droplet disintegrates via jet fission. Repeated evaporation and fission events yield nanometer-sized droplets that carry approximately zR charges. These nanodroplets release gaseous analyte ions which can then be detected by MS.1 The final steps of the ESI process continue to be controversial.2,3 Two limiting scenarios can be considered. Small preformed ions are released from nanodroplets via the ion evaporation mechanism (IEM). This process is based on analyte ejection caused by the high electric field at the droplet surface for rdroplet < 100 Å.1,3,4 In contrast, natively folded proteins follow the charged residue mechanism (CRM). In this scenario, nanodroplets containing a single protein molecule evaporate to dryness. The charge of the vanishing droplet is absorbed by the protein.1 Consistent with the CRM, native proteins produce ions with a composition close to [M + © 2012 American Chemical Society

Received: May 16, 2012 Accepted: July 9, 2012 Published: July 9, 2012 6798

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MODEL JUSTIFICATION Dissociation of Gaseous Protein Complexes. Slow collisional heating of electrosprayed multiprotein assemblies causes ejection of a single subunit that carries a disproportionately large number of excess protons relative to its mass. The mechanism of this asymmetric charge partitioning is well understood (Figure 1a).19−23 Gaseous protein assemblies

to the droplet surface. Most trajectories then have a cationic terminus emerge from the droplet, followed by ejection of the entire chain.29 Similar data were obtained for other polymers.31 Protein ejection via the scenario of Figure 1b is an IEM-type process, mediated by the interplay of Coulombic repulsion and hydrophobicity.29 Unfortunately, the MD studies mentioned here did not employ mobile protons as charge carriers, such that insights into the relationship between conformation and CSDs could not be obtained. Formation of High ESI Charge States for Unfolded Proteins. There are striking parallels between the dissociation of gaseous multisubunit complexes and the ejection of unfolded proteins from ESI droplets (Figure 1). (i) Both parent systems (large protein complex versus solvent droplet) have a size in the nanometer range.7 (ii) Both parent systems carry a net charge that can be estimated from eq 1. (iii) Both processes occur in regions of the mass spectrometer where low-energy collisions with background gas take place (collision cell versus ion sampling interface).32 (iv) Both processes involve “tadpole”shaped intermediates (Figure 1, center panels). (v) Excess protons are highly mobile on the protein and on the droplet surface.24,25 (vi) In both cases an unfolded protein gets ejected that is highly protonated.33 For noncovalent complexes it is undisputed that the high protonation states of the monomeric dissociation product result from charge equilibration prior to the scission point.19−23,26 We propose that similar charge equilibration processes occur during ejection of unfolded proteins from ESI nanodroplets. Specifically, we suggest that rapid equilibration of excess protons between droplet and polypeptide chain is responsible for the high ESI charge states of unfolded proteins (Figure 1b, center panel).

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MODEL IMPLEMENTATION The ESI process of unfolded proteins (Figure 1b) is described using a bead chain model and a continuum charge approximation.34 Similar approaches have been used previously for exploring droplet disintegration28,35 and protein complex dissociation.27 The aqueous nanodroplet that is poised to eject an unfolded protein is described as a sphere with radius rinitial. The excess droplet charge qtot is determined by eq 1, with γ = 0.05891 N m−1. Much of qtot is due to protons, but charged side chains and counterions can also contribute. Initially qtot is evenly distributed on the droplet surface, as required by Gauss’ Law.36 This does not imply that all excess charge carriers reside in the droplet periphery. Instead, solvent polarization will project interior excess charge to the surface.37 Supporting Information Figure S1 illustrates the layout of the system during protein ejection. Each droplet contains a single unfolded chain. Except for steric confinement, the chain adopts a random coil conformation prior to being ejected.38 The protein is modeled as self-avoiding chain consisting of beads with radius r. Each bead represents one residue. Adjacent residue midpoints are 4 Å apart, reflecting the Cα distance in a polypeptide chain. We restrict our considerations to acidunfolded proteins where all carboxylates are neutralized, mimicking commonly used ESI conditions.8,9 Arg, His, Lys, and the N-terminus represent possible gas-phase protonation sites.6 These moieties are designated as chargeable beads, whereas all other residues are neutral. The locations of chargeable beads reflect the sequence of specific proteins. Protein ejection decreases the droplet radius from rinitial to a smaller value r0. The process is subject to conservation of

Figure 1. Cartoon depiction of ESI-MS-related processes. (a) Collision-induced dissociation (CID) of a gaseous protein complex proceeds via unfolding and ejection of a single subunit (red). Charge equilibration causes this subunit to be highly protonated. (b) IEM release of an unfolded protein (red) into the gas-phase from an ESI droplet according to MD simulations.29 Charge equilibration produces a highly charged protein ion, analogous to that in panel a.

initially retain a compact conformation. Activation induces gradual unfolding of a single protein chain. Excess protons on the complex are highly mobile24,25 and they can rapidly transfer between subunits.26 Coulombic repulsion induces charge equilibration, i.e., proton transfer to the subunit that is undergoing unfolding. This charge equilibration lowers the potential energy by maximizing proton−proton distances. Charge transfer to the unfolding subunit occurs up to the ″scission point″ where the subunit detaches.27,28 Ultimately, these events produce a highly charged unfolded protein, and a residual complex that is charge-depleted. MD Simulation Results. Insights into the ESI mechanism of unfolded proteins come from classical molecular dynamics (MD) simulations that employed coarse-grained polymer models (Figure 1b).29 Unfolding exposes numerous nonpolar side chains to the solvent.30 The hydrophobicity is further increased in the case of acid-induced denaturation, where carboxylates are converted to neutral moieties by protonation. At pH 2 only cationic sites are retained. MD simulations29 reveal that these unfolded chains initially prefer positions close 6799

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volume, with a density of ρ = 1 g cm−3 for water and protein.5 The volume of a folded protein is M/ρ, where M is the protein mass.5 The value of r is chosen accordingly. Changes in droplet radius caused by solvent evaporation are negligible during the short time interval of a protein ejection event.29,31 The electrostatic energy V of the system is27,28,35 V=

⎛ 1 ⎜1 4πε0 ⎜⎝ 2

N

∑ i=0

qi 2 ri

N−1

+

N

∑ ∑ i=0 j=i+1

qiqj ⎞ ⎟ rij ⎟⎠

Information Figure S1). A droplet radius of rinitial = 65 Å is used, corresponding to an excess charge of qtot/e = 59 protons. Protein ejection reduces the droplet radius to r0 = 64.5 Å. We will first consider the case where the protein emerges from the surface as a linear chain. Protein ejection is a stepwise process where one charged residue emerges after another (N = 1, ... 30). The protonation pattern within the system changes as the number of ejected residues increases (Figure 2a). For N = 6 almost all protonation sites outside the droplet are fully charged (qi/e ≈ 1). At the scission point (N = 30), only the terminal sites are fully protonated, while residues closer to the droplet carry less charge. During ejection the charge on the expelled chain increases up to zprotein = 24.9 at the scission point (Figure 2b), reflecting the charge equilibration that has been postulated in Figure 1b. After rounding, it is seen that this particular ESI event would produce a [M + 25H]25+ ion. The electrostatic energy V(N) of the system decreases during ejection as a result of charge redistribution. The lowest energy is attained for N = 30 (Figure 2c). This linear chain scission point energy will be denoted as V*. It provides a reference for a given value of rinitial, and the electrostatic energy can be reported as

(2)

where the index i refers to chargeable entities only. The droplet corresponds to i = 0, whereas protonation sites are designated as i = 1, 2, ..., N (Supporting Information Figure S1). N represents the number of chargeable residues that have been expelled at any given stage. At the scission point N equals the total number of chargeable residues. The charge on entity i is qi, and the corresponding radius is ri. The values rij refer to the pairwise midpoint distances between entities i and j. The first term in eq 2 reflects the energy associated with accumulating a charge qi on a spherical entity i. The double sum accounts for repulsion between all charged residues, as well as repulsion between charged residues and droplet. Charge residing on protonated residues that have not yet emerged from the droplet constitutes part of q0.37 Mobile charge carriers will rapidly distribute into a pattern that minimizes the overall electrostatic energy.36 Thus, the charge configuration q0, ..., qN will always correspond to the lowest possible V(N).28,35 Charge (proton) transfer takes place until the entire chain has emerged and is about to separate from the droplet. This scission point determines the final protein charge qprotein according to qprotein = qtot − q0 (3) with an experimentally observable ESI protonation state qprotein z protein = e

ΔV = V − V *

(5)

such that ΔV = 0 for N = 30 (Figure 2c). The energy will decrease further after the protein has separated from the droplet.27 However, zprotein remains constant after the scission point and therefore the ΔV < 0 regime is irrelevant for our considerations. Linear Chain Ejection from Differently Sized Droplets. Using the same linear chain model as above zprotein was calculated as a function of rinitial (Figure 2d, solid line). Droplets with radii between 1 μm and 100 Å yield zprotein values between 27 and 29. For smaller droplets zprotein diminishes rapidly, reflecting the decrease in qtot (eq 1). The minimum value of rinitial is determined by the hypothetical case where the “unfolded” chain is completely collapsed into a sphere inside the droplet. For the case considered here this corresponds to rinitial = 18.9 Å. Accommodating the chain in such a small droplet is an unlikely scenario; we discuss this case only to estimate the lower bound of permissible droplet sizes. As expected, zprotein for these smallest droplets is identical to the Rayleigh charge state zR = 9 of the folded protein. Nonlinear Protein Structures. Linear chain conformers demonstrate basic features of the model. Realistically, however, the protein will be able to adopt various scission point conformations. The effects of these structural differences are illustrated in Figure 3a−c, using the same protein sequence as before (N = 30, rinitial = 65 Å). The linear case is included for comparison (zprotein = 25, ΔV = 0, Figure 3a). A partially collapsed chain leads to a lower charge state of 17 with an electrostatic energy of ΔV = 1791 kBT (Figure 3b). Further coiling reduces zprotein to 12, with ΔV around 3000 kBT (Figure 3c). These data demonstrate that any deviation from a linear protein structure will reduce the number of protons on the departing chain. The abundance of various conformers can be estimated by assuming that the scission point ensemble obeys a Boltzmann distribution. MC sampling39 was used to identify structures that are thermally accessible. It is found that, despite some conformational variability, there is a strong prevalence for structures that point away from the droplet center in an almost

(4)

Energy minimization is subject to the condition that no residue can carry more than a single elementary charge. The calculated zprotein values are noninteger numbers that are interpreted as ensemble-averaged charges. When appropriate, calculated zprotein values will be rounded to the nearest integer for comparison with measured protonation states.

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METHODS Mass spectra of myoglobin (Mb) and cytochrome c (cyt c) were recorded under standard ESI conditions. All software was written in-house, building on Fortran code that had previously been used for other applications.27,5 Conformational sampling at the scission point was performed using a Metropolis Monte Carlo (MC) approach.39 A temperature of T = 373 K was used, reflecting the presence of heating elements in the ion source of the mass spectrometer. For modeling CSDs of Mb and cyt c the chain lengths and positions of protonation sites were chosen in accordance with the protein sequences. Additional details can be found in the Supporting Information.

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RESULTS AND DISCUSSION Model Behavior for Linear Chains. We will initially explore the case of a hypothetical 17 kDa protein that is unfolded and consists of 150 residues. Every fifth residue can be protonated, for a total of 30 chargeable sites (Supporting 6800

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Figure 3. (a−c) Hypothetical scission point structures for protein ejection from a droplet with rinitial = 65 Å. Each panel lists the ESI charge state zprotein and the electrostatic energy ΔV. (d) Overlay of 20 representative scission point structures, taken from a Monte Carlo ensemble.

Coulombic repulsion between droplet and protein corresponds to a force of ∼300 pN; intrachain repulsion amounts to an additional ∼2000 pN. For comparison, the force required for stretching proteins mechanically is only ∼100 pN.40 The absence of coiled scission point structures is also supported by MD data.29 All conformers in Figure 3d have zprotein = 24, only slightly lower than for the fully linear scenario of Figure 3a. The average energy of the MC ensemble (Figure 3d) is around 190 kBT. Despite their lower energy (ΔV = 0), perfectly linear chains are thermodynamically disfavored because they have an entropy of zero. The MC ensemble reflects energetic and entropic contributions at T = 373 K. Linear chains (Figure 3a) represent the T = 0 conformation. The fact that very similar zprotein values are obtained in both cases shows that the model predictions are not strongly temperature dependent. MC sampling was used to determine the dependence of zprotein on droplet size. The charge states predicted in this way are almost identical to those of linear chains for all values of rinitial (Figure 2d, open symbols). Width of CSDs. Unfolded proteins generally show very wide CSDs.8−12,14−16,41 It is worth considering whether this behavior can be caused by protein structural heterogeneity at the scission point. For the chain considered in Figure 3a−c with rinitial = 65 Å, it was seen that different scission point structures can, in principle, give rise to a wide range of zprotein. However, MC sampling revealed that extensively coiled structures are inaccessible due to free energy considerations (Figure 3d). As a result, protein ejection for any given droplet size will generate ions that cover no more than two adjacent protonation states (Figure 2d, open symbols). Thus, conformational differences at the scission point are not a major contributor to ESI protonation heterogeneity for completely denatured proteins. Figure 2d reveals that protein ejection f rom dif ferently sized droplets is the main cause of charge state heterogeneity. The ESI source region contains a steady-state droplet population covering sizes from micrometers to nanometers.42 Our model

Figure 2. (a−c) System parameters during ejection of a linear protein chain with 30 protonable residues from a droplet with rinitial = 65 Å. (a) Average protonation state of chargeable residues for N = 6, N = 22, and N = 30. (b) Charge accumulation on the protein as N = 1, ... 30 chargeable residues emerge from the droplet. (c) Reduction in electrostatic energy ΔV accompanying protein ejection, in units of kBT (kB is the Boltzmann constant). (d) ESI charge state of an unfolded protein (N = 30) for different rinitial. Solid line: linear chain; open symbols: Monte Carlo ensemble.

linear fashion (Figure 3d). This behavior reflects the radial symmetry of the droplet electric field, as well as the tendency of the system to maximize charge−charge distances. Also, 6801

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predicts that small droplets produce ions with lower charge states, whereas large droplets generate higher values of zprotein (Figure 2d). The width of the CSD is determined by the droplet size range that is capable of protein ejection. The ejection process commences with the first chargeable residue that emerges from the surface (N = 1). The electrostatic force acting on this residue will then trigger ejection of the rest of the chain.29 The N = 1 nucleation event must be governed by factors similar to the ejection of small ions in the classical IEM.1,4,43,44 Specifically, ejection of a charge carrier is driven by the electric field E that emanates from the droplet surface 1 q0 E= 4πε0 d 2 (6) where d is the distance from the droplet midpoint. With q0 ≈ zR e, d ≈ rinitial and eq 1, we find that ⎛ γ ⎞1/2 E = 2⎜ ⎟ ⎝ ε0rinitial ⎠

(7)

The field strength required for ion ejection is achieved for Rayleigh-charged droplets with rinitial ≈ 100 Å,1,3,4 corresponding to E = 1.6 V nm−1. Our considerations imply that ejection of unfolded proteins is viable for droplets with a maximum radius around 100 Å. The minimum possible rinitial value is determined by the chain dimensions, as discussed above. A value of 18.9 Å was obtained for the protein considered in Figure 2. Thus, the permissible rinitial range for protein ejection is ∼100 to 18.9 Å, resulting in ESI charge states between 28 and 9 (Figure 2d, highlighted in red). Predicting the ion abundance of individual ESI charge states requires knowledge of the droplet size distribution, as well as the dependence of the protein ejection rate on rinitial. Our model cannot provide information regarding the former, but the latter can be examined in a qualitative fashion. Starting with the upper bound of rinitial = 100 Å, protein ejection will become more favorable for smaller droplets due to the (rinitial)−0.5 dependence in eq 7. Smaller droplets should also enhance protein ejection by entropic confinement. Thus, the ejection efficiency will rise with decreasing rinitial up to a maximum value. Beyond this value, the trend will reverse because many droplets with rinitial ≪ 100 Å will have undergone protein ejection at an earlier point in their life cycle. Also, protein ejection has to compete with IEM emission of small charge carriers.4 Thus, both the largest (100 Å) and the smallest droplets will contribute relatively little to the mass spectrum. Protein ejection should be most prevalent for droplet sizes somewhere in-between these two extremes. It will be seen that this prediction is confirmed by analyses of experimental data (see below, Figures 4d and 5d). Experimental ESI Mass Spectra. The performance of our IEM/charge equilibration model is illustrated for Mb (17 kDa) and cyt c (12 kDa). At pH 7, both proteins adopt a globular fold, whereas exposure to pH 2 induces near-complete unfolding. The two proteins commonly serve as test compounds in ESI-MS, and their behavior resembles that of many other species.12 ESI of native Mb yields [M + zH]z+ ions in a narrow distribution centered at z = 9. The CRM/Rayleigh charge theory (eq 1)1,5−7 predicts an average charge of zR = 9.5, which matches the experimental data quite well (Figure 4a). Solution-

Figure 4. (a) ESI mass spectrum of native Mb (pH 7). Protonation states are indicated as 10, 9, etc. Also shown is the Rayleigh charge zR expected for the folded conformation. (b) ESI mass spectrum of unfolded Mb (pH 2). (c) Protein charge state zprotein predicted for differently sized ESI droplets. Droplets with radii between 100 and 18.9 Å highlighted in red) are predicted to produce gaseous protein ions. (d) Relative contribution of differently sized droplets to the protein ion population. The data in c and d reproduce the experimental spectrum (red circles in panel b).

phase unfolding of Mb results in a much wider CSD that has its maximum at z = 19 (Figure 4b). Mb contains 33 protonation sites. MC simulations were performed to determine the dependence of zprotein on rinitial for the unfolded state (Figure 4c). As outlined above, droplets with rinitial between 100 Å and 18.9 Å are expected to eject protein ions. The corresponding zprotein values predicted by the model range from 26 to 9 (Figure 4c, red). This prediction is in close agreement with the experimentally observed values (26−8, Figure 4b). A linear combination strategy can be used for determining the contribution of each droplet size to the overall ESI mass spectrum. The measured peak intensities form a vector s = (s1, s2, ..., sk, ...) where sk represents the peak intensity of charge state k (Figure 4b, red circles). The zprotein values predicted by the model are placed in a matrix Z with columns zn = (z1, z2, ... zk, ...)n. The index variable n represents a narrow bin of rinitial values. Each matrix element zkn represents the contribution of 6802

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lower molecular weight of cyt c, relative to Mb. The charge states predicted for unfolded cyt c fall between 20 and 7 (Figure 5c, red symbols), which exactly matches the experimentally observed range (Figure 5b). The size distribution of proteinemitting droplets has its maximum close to rinitial = 50 Å (Figure 5d), similar to the Mb distribution (Figure 4d). Slight differences in these an distributions will reflect the physicochemical properties of the two proteins.

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CONCLUSIONS The ESI charge states of globular proteins can be estimated on the basis of eq 1. The beauty of this CRM/Rayleigh charge model lies in its simplicity; native proteins are considered to be spheres with an ESI charge corresponding to zR of an equally sized water droplet.1,5−7 A comparable strategy for predicting the ESI behavior of unfolded proteins has been lacking so far. The current work addresses this issue by developing a minimalist IEM/charge equilibration model. Similar to the CRM, our approach disregards atomistic details. Instead, the unfolded protein is described as a bead chain. Ejection is accompanied by charge equilibration between droplet and protein. CSDs predicted in this way agree remarkably well with experimental data, providing support for the model. Solution additives such as sulfolane45 and m-nitrobenzyl alcohol46 can enhance ESI protonation to some extent. Two mechanisms have been proposed for this “supercharging” effect. In one scenario the supercharging agent raises the surface tension, such that the droplet will accommodate more protons (eq 1). In our model, zprotein is proportional to the droplet charge, and therefore an increased γ will shift the CSD to higher values. In the second scenario, supercharging agents facilitate protein unfolding within the ESI droplet.46 This change will switch the ESI mechanism from the CRM to the IEM (Figure 1b). The latter pathway results in higher charge states. Hence, supercharging can readily be accommodated in our model. The calculations of this work apply specifically to proteins that form a random coil in bulk solution.38 We found that under these conditions ESI protonation heterogeneity is caused almost exclusively by ejection from differently sized droplets. An additional source of charge state heterogeneity may be encountered if protein samples encompass different degrees of unfolding (e.g., due to partial retention of secondary structure). Semidenatured conformers give rise to somewhat lower ESI charge states than random coil chains.14 This effect can be explained if partially structured regions survive until the scission point is reached, resulting in a lowering of zprotein (Figure 3b and c). A related scenario is encountered when samples contain a mix of native and denatured proteins. ESI of these samples will generate two populations of nanodroplets that contain either folded or unfolded chains. The former will produce low charge states (CRM), whereas the latter will form high charge states (IEM), resulting in bimodal CSDs that are well documented experimentally.8,14 Even the mass spectra of extensively unfolded proteins encompass charge states comparable to the native state, albeit at very low intensities (Figures 4b and 5b). It cannot be decided whether these ions originate from collapsed solutionphase conformers that follow the CRM, or via ejection from very small droplets. In the limit of highly collapsed protein structures and/or droplets close to the minimum permissible radius both models predict the same charge states (Figure 2d). A small number of ions might also be formed from droplets

Figure 5. ESI mass spectra of native cyt c at pH 7 (a) and unfolded cyt c at pH 2 (b). (c) Dependence of zprotein on droplet size. (d) Contribution of droplet size bins to protein ejection. Additional information can be found in the caption of Figure 4.

droplet size n to charge state k (Figure 4c). The experimental spectrum s is given by s = Z × a. This relationship allows determining the vector a = (a1, a2, ... an, ...) that contains the relative contribution of each rinitial value to the experimental spectrum (Figure 4d). Using this matrix-vector strategy, it is possible to uncover the extent to which differently sized droplets contribute to the production of gaseous Mb ions (Figure 4d). It is seen that droplets with rinitial around 50 Å provide the highest contribution. Protein ion ejection gradually decreases for droplets with larger and with smaller radii. Spikes in the distribution originate from the conversion of calculated fractional charges to discrete protonation states. Most importantly, the overall bell-shaped appearance of the distribution is consistent with the expectations outlined in the previous section. The data of Figure 4d, in combination with the zprotein progression of Figure 4c, reproduce the experimental spectrum (Figure 4b, red circles). Native cyt c forms ions in charge states 8 and 7, consistent with zR = 7.9 as estimated using eq 1 (Figure 5a). Acid-induced unfolding yields a wide CSD centered around 15 (Figure 5b). Cyt c ions will be emitted from droplets with rinitial between 100 and 17 Å. The slightly different droplet size range reflects the 6803

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below the Rayleigh limit. We consider these issues to be secondary, because the corresponding signals are very weak. Future refinements of our model may include a more detailed description of the polypeptide chain, with protonation sites that are characterized by different gas-phase basicities. Also, it will be interesting to explore in more detail how ESI proceeds for semidenatured proteins and in the presence of supercharging agents. Effects of different droplet sizes in ESI and nanoESI1 could represent another aspect that is worth investigating.

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ASSOCIATED CONTENT

* Supporting Information S

Additional material as described in the text. This material is available free of charge via the Internet at http://pubs.acs.org.

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AUTHOR INFORMATION

Corresponding Author

*Telephone: (519) 661-2111 ext. 86313. E-mail: konerman@ uwo.ca. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS Funding was provided by the Natural Sciences and Engineering Research Council of Canada, the Canada Foundation for Innovation (CFI), and the Canada Research Chairs Program.

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REFERENCES

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dx.doi.org/10.1021/ac301298g | Anal. Chem. 2012, 84, 6798−6804