Use of Fourier Transform for Deconvolution of the Unresolved

Anal. Chem. 2004, 76, 127-136

Use of Fourier Transform for Deconvolution of the Unresolved Envelope Observed in Electrospray Ionization Mass Spectrometry of Strongly Ionic Synthetic Polymers Benjamin S. Prebyl and Kelsey D. Cook*

Department of Chemistry and Measurement & Control Engineering Center, University of Tennessee, Knoxville, Tennessee 37996-1600

Fourier transform analysis of electrospray mass spectra of synthetic polymers can be used to obtain information about the monomer mass, charge distribution, and polydispersity in cases where the convolution of molecular weight, charge, and isotope distributions renders spectra otherwise uninterpretable. Charge-state information can be used with the original mass spectrum to estimate the sample average molecular weight. Determination of the combined end group mass may also be feasible, but at best, an average value can be derived in cases where multiple end groups or adducting species are present. The method is tested using simulated and experimental spectra. Successful application requires a reasonable signalto-noise ratio and spectral digitization rate but does not require full resolution of contributing peaks. It appears in this regard to be complementary to the autocorrelation method of Danis and Huby (Danis, P. O.; Huby, F. J. J. Am. Soc. Mass Spectrom. 1995, 6, 1112-1118). A hallmark and enabling feature of electrospray mass spectrometry (ES MS) is its ability to sample and detect multiply charged ions.1 While the presence of various different charge states complicates the appearance of ES spectra, several “chargestripping” approaches have emerged for deconvolving the resulting spectra of multiply charged species.2-16 These methods are * Corresponding author. E-mail: [email protected]. Phone: (865) 974-8019. (1) Fenn, J. B.; Mann, M.; Meng, C. K.; Wong, S. F.; Whitehouse, C. M. Mass Spectrom. Rev. 1990, 9, 37-70. (2) Mann, M.; Meng, C. K.; Fenn, J. B. Anal. Chem. 1989, 61, 1702-1708. (3) Ferrige, A. G.; Seddon, M. J.; Jarvis, S. Rapid Commun. Mass Spectrom. 1991, 5, 374-377. (4) Ferrige, A. G.; Seddon, M. J.; Green, B. N.; Jarvis, S. A.; Skilling, J. Rapid Commun. Mass Spectrom. 1992, 6, 707-711. (5) Ferrige, A. G.; Seddon, M. J.; Skilling, J.; Ordsmith, N. Rapid Commun. Mass Spectrom. 1992, 6, 765-770. (6) Dunn, W. J., III; Emery, S. L.; Glen, W. G.; Scott, D. R. Environ. Sci. Technol. 1989, 23, 1499-1505. (7) Georgakopoulos, C. G.; Statheropoulos, M. C.; Montaudo, G. Anal. Chim. Acta 1998, 359, 213-225. (8) Hagen, J. J.; Monnig, C. A. Anal. Chem. 1994, 66, 1877-1883. (9) Ioup, J. W.; Ioup, G. E.; Rayborn, G. H., Jr.; Wood, G. M., Jr.; Upchurch, B. T. Int. J. Mass Spectrom. Ion Processes 1983, 55, 93-109. (10) Pearcy, J. O.; Lee, T. D. J. Am. Soc. Mass Spectrom. 2001, 12, 599-606. (11) Raznikov, V. V.; Raznikova, M. O. Int. J. Mass Spectrom. Ion Processes 1991, 67-79. (12) Raznikov, V. V.; Raznikova, M. O. Int. J. Mass Spectrom. Ion Processes 1985, 63, 157-186. 10.1021/ac0348266 CCC: $27.50 Published on Web 11/20/2003

© 2004 American Chemical Society

generally limited, however, to spectra obtained from single analytes or relatively simple mixturessfar from the case encountered in applications to synthetic polymers, which are intrinsically complex mixtures of components of varying degrees of polymerization. Indeed, polymer applications were among the first attempted by ES MS,17 and the resulting spectral complexity spurred some early skepticism about the method’s potential.18 While the power of ESsespecially for analysis of biomaterialssis now far beyond dispute, polymer applications remain relatively rare and challenging.19 Figure 1 illustrates the complexity of polymer ES spectra with data from some of the early work of Fenn and co-workers.1 For low-mass poly(ethylene glycol) (PEG; Figure 1a), the spectrum is dominated by a series of singly charged ions (z ) 1) at mass intervals (h) corresponding to the monomer mass (44.0 Da). Although potentially complicated by some sampling or instrumental bias (which may depend on source conditions, inter alia19), this “envelope” to first order can be taken to represent the sample molecular weight distribution, and the combined end group mass can be estimated from the “residual” mass (m - (hi) - k, where m is the ion mass, i is the degree of polymerization, and k is the mass of any adducting ion; e.g., k ) 23 for Na+). As the average mass increases, the spectrum becomes more complicated by the appearance of more highly charged oligomer ions (Figure 1b and c). By the time the nominal molecular weight reaches 3350 (Figure 1d), individual charge states are no longer discernible and the spectrum apparently degenerates to an unresolved envelope.1,20 Recognizing the periodicity of spectra like those of Figure 1ac, Danis and Huby21 attempted to use the tools of autocorrelation and Fourier transformation to facilitate interpretation of polymer (13) Yates, J. R., III; Morgan, S. F.; Gatlin, C. L.; Griffin, P. R.; Eng, J. K. Anal. Chem. 1998, 70, 3557-3565. (14) Zheng, H.; Ojha, P. C.; McClean, S.; Black, N. D.; Hughes, J. G.; Shaw, C. Rapid Commun. Mass Spectrom 2003, 17, 429-436. (15) Reinhold, B. B.; Reinhold, V. N. J. Am Soc. Mass Spectrom. 1992, 3, 207215. (16) Zhang, Z.; Marshall, A. G. J. Am Soc. Mass Spectrom. 1998, 9, 225-233. (17) Dole, M.; Mack, L. L.; Hines, R. L.; Mobley, R. C.; Ferguson, L. D.; Alice, M. B. J. Chem. Phys. 1968, 49, 2240-2249. (18) Maekawa, M.; Nohami, T.; Zhan, D.; Kiselev, P.; Fenn, J. B. J. Mass Spectrom. Soc. Jpn. 1999, 47, 76-83. (19) Hunt, S. M.; Sheil, M. M.; Belov, M.; Derrick, P. J. Anal. Chem. 1998, 70, 1812-1822. (20) Wong, S. F.; Meng, C. K.; Fenn, J. B. J. Phys. Chem. 1988, 92, 546-550. (21) Danis, P. O.; Huby, F. J. J. Am. Soc. Mass Spectrom. 1995, 6, 1112-1118.

Analytical Chemistry, Vol. 76, No. 1, January 1, 2004 127

Figure 1. Mass spectra of PEG at a concentration of 0.05 µg/µL in 50:50 methanol/water injected at a rate of 7 µL/min. Major peaks are associated with oligomer-Na+ adducts. PEG nominal molecular weight (a) 400, (b) 1000, (c) 1450, and (d), 3350. The respective charge states are marked with Roman numerals. (Adapted with permission from ref 1).

mass spectra obtained using field desorption and fast atom bombardment. These ionization methods generally provide only singly charged ions, and Danis and Huby found that autocorrelation was better able than Fourier analysis to determine end group masses and monomer ratios from resolved spectra of singly charged copolymers. The method was effective provided that resolution was adequate to discern individual oligomers; autocorrelation of spectra of higher-mass materials was not successful. As evident from Figure 1, the occurrence of multiple charging compromises the ability to resolve oligomers even at relatively low mass. The applicability of autocorrelation for polymer ES is therefore likely to be limited; indeed, in the early stages of this research, we considered and then abandoned an autocorrelation approach. We revisit now the potential utility of Fourier transformation (FT) for interpreting polymer mass spectra and particularly for polymer ES spectra. FT methods have been used elsewhere for simplifying conventional (as opposed to ion cyclotron resonance, ICR) mass spectra. For example, Raznikov and Raznikova used FT followed by data manipulation and inverse FT of unresolved isobar envelopes to reveal the various isobaric contributors and their relative abundances.11,12 Ioup et al. used FT methods to increase the effective resolution obtained from a 5-in.-radius Dempster-type magnetic deflection mass spectrometer.9 To our knowledge, the work of Danis and Huby21 discussed above remains the only report to date of an attempt to apply FT to a conventional (non-ICR) polymer mass spectrum. They concluded that aliasing and sparse data sets limited applicability. This study seeks to assess whether the enhanced spectral richness afforded 128 Analytical Chemistry, Vol. 76, No. 1, January 1, 2004

by ES sampling and the improved spectral sampling afforded by faster computers might enhance applicability for interpretation of unresolved, multiply charged ES MS spectra of strongly ionic homopolymers. Testing will involve both simulated and experimental polymer spectra. EXPERIMENTAL SECTION All simulations and computations were performed using a Dell (Round Rock, TX) computer equipped with Windows 2000 Professional (Microsoft, Seattle, WA) and a 1.7-GHz Pentium IV processor. Synthetic homopolymer data were simulated with Sigma Plot 2000 (SSPS Inc., Chicago, IL) software using simple combinations of sine and Guassian functions, utilizing a range of 0-4000 m/z with either 5000 or 15 000 uniformly spaced data points (point spacing 0.8 or 0.27 m/z), as noted. This number of points was comfortably within the “64K” data capacity of Microsoft Excel 2000, while easily meeting the Nyquist criterion for all periods expected in the FT output.22 Polydispersity (PD) was calculated as the ratio of the weight-average to the number-average molecular weight;23 the average molecular weights were determined using all mass-intensity pairs from the simulation. Random numbers for noise simulations were generated with Excel. Discrete Fourier transformation22 was accomplished using the fast Fourier transform (FFT) algorithms included with MATLAB (The Mathworks Inc., Natick, MA) software version 6.0.0.88 release 12. FFT calculations required computation times of less than 5 s. (22) Briggs, W.; Henson, V. The DFT; Society for Industrial and Applied Mathematics: Philadelphia, 1995. (23) Stevens, M. P. Polymer Chemistry: An Introduction, 3rd ed.; Oxford University Press: New York, 1999.

Negative-ion electrospray mass spectra were obtained using a Quattro II (Micromass, Manchester, U.K.) triple quadrupole mass spectrometer equipped with a “Z-source”. Data acquisition was accomplished with the Micromass MassLynx software package (version 3.4). Multichannel acquisition spectra were acquired over the m/z region 100-1400 summing 700 scans/spectrum with a scan rate of 5 s/scan and 16 points per m/z unit. Mass spectra were acquired with a capillary voltage of -2500 V, nitrogen as the nebulizing gas (20 L/h) and drying gas (300 L/h), and source block and desolvation temperatures of 110 and 150 °C, respectively. The cone voltage was -30 V for all experiments. Ion exchange was performed with a 70-mL bed volume of Amberlite IR-120 cation exchanger (Acros, Atlanta, GA) pretreated with concentrated H2SO4 to ensure that it was in the acid form and then rinsed with water. About 0.1 g of sodium poly(styrenesulfonate) (average molecular weight 4600; Pressure Chemical Co., Pittsburgh, PA) was dissolved in 2 mL of deionized H2O (Milli-Q system, Millipore, Bedford, MA), loaded on to a 5 × 60 cm column, and gravity eluted with deionized water (∼0.5 mL/min). Samples (∼10 mL each) were collected until twice the bed volume had eluted and were then lyophilized and combined. A 10 µM concentration of poly(styrenesulfonate) was prepared in 50/50 v/v methanol/water (both solvents were HPLC grade, Aldrich, Milwaukee, WI), with or without 200 µM NaOH or 200 µM H2SO4 (reagent grade, Aldrich). Sample solutions were loaded into a 250-µL syringe (SGE, Austin, TX) and infused directly into the probe via a fused-silica capillary (300-µm o.d., 50-µm i.d.; Polymicro Technologies, Phoenix, AZ) at 5 µL/min using a Harvard Apparatus (Holliston, MA) model 22 syringe pump. RESULTS AND DISCUSSION General Considerations. Key aspects of the periodicity of a polymer mass spectrum (evident in Figure 1) are illustrated in Figure 2, which represents a simplistic mass spectrum composed of six peaks of equal intensity spaced at 1 Da (Figure 2b), convolved with a resolution function (Figure 2a) whose base width approaches the peak separation. The resulting spectrum (Figure 2c) takes on the appearance of a (truncated) sine wave. For a polydisperse polymer sample with a given combined end group mass (), the periodicity can be related to the charge (z) and the monomer mass (h, as above), such that for an oligomer of degree of polymerization i

(m/z)i ) [(ih) + E]/z

(1)

where E ()  + zk) represents the combined mass of the end groups () plus any adducting ions (e.g., as above, k ) 23 for Na+; for deprotonation of an acidic ionic polymer, k ) -1). Since E is constant for a given charge state, it will affect the phase (offset) of the distribution but not the period (peak separation) for a given charge state. It can be seen that the period for charge state z will be h/z, and the offset will be E/z. If multiple charge states are present, the overall spectrum will comprise the superposition of separate distributions with different periods and offsets for each charge state. FFT of Simulated Data. Single Charge State. The application of FFT was tested first with simulated data for a polymer of 40 000 average molecular weight, with a monomer mass of 160 Da and

Figure 2. (a) Simulation of a typical peak shape obtained from a quadrupole mass spectrometer tuned to a baseline width of 1 Da. (b) Hypothetical “infinite resolution” mass spectrum composed of six evenly spaced peaks. (c) Result of convoluting (a) with (b) to generate a more realistic approximation to an experimental spectrum. Even spacing gives this spectrum a sinusoidal appearance.

PD of 1.002 (corresponding to ∼70 peaks above 1% relative intensity). For simplicity in initial tests, it was assumed that there was a single charge state (z ) +13) and no end groups or adducting ions (E ) 0). The simulated spectrum (Figure 3a) was created using eq 2, where x represents the mass-to-charge ratio

f (x) ) (c + (sin(πx/p))2)(y0 + a exp(-0.5(x - xo)/b)2) (2)

(m/z) and f (x) represents intensity or abundance. The p parameter represents the period (h/z, as defined above); it can be manipulated to allow for simulation of different charge states or monomer masses. The sine term is squared to remove negative values (corresponding to negative intensities, which would not be Analytical Chemistry, Vol. 76, No. 1, January 1, 2004

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Figure 3. (a) Simulated electrospray mass spectrum of a hypothetical 40-kDa homopolymer with a 160-Da repeat unit, charge state of +13, and polydispersity of 1.002. The data were obtained from eq 2 with the following parameters: a, b, c, p, x0, xmin, xmax, sample spacing, and y0 equal to 10 000, 142, 2, 12.31, 3076.9, 0, 4000, 0.8, and 0, respectively. (b) Result of FFT of the data of (a), zero-filled to 213 points prior to transformation. (c) Magnified region of the FT in (b) over the period range of 2-14 m/z. (d) Comparison of the FT shown in (c) (dotted line) with data for a similar simulation with a polydispersity of 1.009 (solid line). (e) Comparison of estimated values of E for sampling intervals of 0.8 (1) and 0.27 (b) with increasing zero filling.

meaningful in a mass spectrum). Parameters a and b describe a Gaussian function whose width (determined by b) relates to the polydispersity and whose height (determined by a) relates to peak abundance. The c term mimics the deviations from baseline that result from incomplete resolution of adjoining members of a series (baseline-resolved data may be simulated by setting c to 0); it is offset by the y0 term, which restores the Gaussian to baseline at high and low m/z. Finally, x0 determines the center of the polymer distribution. This approach to simulation neglects specific contributions from isotopic distributions. The resulting simulated spectra generally resemble what would be expected for a relatively lowresolution analyzer, such as a quadrupole. It should be noted, however, that use of a fixed sine wave frequency artificially increases effective resolution at higher mass, since the peaks would otherwise be expected to broaden with increasing contribu130 Analytical Chemistry, Vol. 76, No. 1, January 1, 2004

tions from heavy isotopes. However, the peak positions and separations remain those that would be expected based on h being the average monomer mass (carbon mass 12.011, etc.)sa realistic approximation for unresolved polymer envelopes. The MATLAB FFT function requires 2n input data points, where n is an arbitrary integer. In Figure 3a, eq 2 was modeled for 5000 x values spaced at 0.8 m/z unit. The nearest n value would be n ) 13 (213 ) 8192), requiring that 3192 zero-valued points be appended at the end of the significant data. This “zero filling” improves the FFT performance by effectively lengthening the m/z axis, thereby decreasing the spacing of the period values after FFT. The resulting FT (Figure 3b) provides output data over the period range of 1.6 (2 times the data spacing) to 6553.6 m/z (the total m/z range or 0.8 × 8192 ) 6553.6). A plateau at high-m/z periods dominates the FT. This plateau relates primarily to the apodization and zero-filling functions; our focus is therefore on

the relatively low intensity, low-m/z period region (Figure 3c), which contains the desired information about the spectral period and the monomer mass. The maximum of the single peak in the transform (for n ) 13) falls at a period p ∼12.32, corresponding nicely to the hypothetical monomer mass divided by the charge state (h/z ) 160/13 ∼ 12.31). The small error results from the finite spacing of the discrete points in the FT. The error can be reduced or eliminated by extrapolation between points, which is most easily accomplished by plotting the derivative of the FT plot (the socalled “dispersion mode” FFT), in which case the peak position coincides with a zero crossing at 12.31. Alternatively, the spacing between points can be reduced by increased zero filling; n values above 14 provided estimated monomer masses within 0.01 Da of the input value. We therefore chose to expand the data to 215 ) 32 768 input data points for all subsequent calculations, except where noted. Absent the addition of noise (see below), it was not possible to estimate the precision of the transform value. It is noteworthy that the accuracy of h can exceed the precision (0.8 Da) of the input datasa consequence of deriving a single h value from all of the input data. The width of the FT peak is inversely proportional to the number of periods sampled; for a pure sine wave, sampling an infinite number of periods gives a δ function (infinitesimal peak width) for the FT peak.22 The polydispersity should therefore be reflected in the width of the FT peak. Figure 3d compares the FT results of Figure 3c with results for a similar simulation with a polydispersity of 1.009 (increasing b in eq 2 from 142 to 314). This small (0.007) increase in polydispersity corresponds to increasing the number of peaks above 1% relative intensity from 70 to 160. The width of the FT peak at the base (1% intensity) decreases from 0.75 to 0.45 upon increasing the polydispersity. At half-height, the width of the FT peak decreases from 0.29 to 0.14. Both changes are readily discernible and could be used to estimate the polydispersity, given suitable calibration standards. (It should be noted that sampling or analyzer mass bias may introduce significant errors in measured polydispersity, unless suitable calibration standards are available.24) The MATLAB program also provides the phase of the output (φ) at each value of x; in Figure 3c, φ(12.31) ∼ 0.14 rad. This can be used to estimate E, the combined total end group and adduct mass:

E ) (φ/2π)pz

(3)

In this case, E ∼3.6 Da; the “correct” value for the simulation would be 0. If an arbitrary end group mass of 104.0 is added to the contrived homopolymer described above (by simply adding 104/13 ) 8 to each x value), the data of Figure 3c is not affected (the peak remainssas it shouldsat ∼12.31), but the associated phase shifts to 4.22 rad, corresponding to an apparent end group mass of 107.5 Da. The small inaccuracy of both end group estimates results from the fact that we are using discrete (digital) sampling to approximate f (x), rather than evaluating a truly continuous (analog) function. As a result, we must use a discrete FFT algorithm, by which the amplitude and phase of the transformed spectrum (Figure 3b and c) are only evaluated and (24) Hanton, S. D. Chem. Rev. 2001, 101, 527-569.

reported at discrete values. It can be shown that only in the unlikely event that there are an exact, integral number of sampling points in each period of the normal spectrum (i.e., only if p/w is an exact integer, where w is the interval between sampled m/z values in Figure 3a) will the peak maximum in Figure 3c exactly match p. If this condition is not met, the estimate of E derived from φ at the approximate peak position will also be slightly in error. Multiplication by p and z (eq 3) amplifies the error. Decreasing the sampling interval from 0.8 to 0.27 Da while retaining 215 input points decreases the total input m/z range by almost 60%, thereby diminishing the period resolution and affording a poorer φ estimate (Ecalc ) 21.3 Da for Esimulated ) 0). Increased zero filling decreases the interval between period points in the transform and improves the accuracy of the phase calculation.22 Figure 3e shows that the derived E values approach the expected value when n ) 17 or 18 for Esimulated ) 0 using the 0.8 or 0.27 sampling interval, respectively, and vary little at higher n. Similar results were obtained when Esimulated ) 104 Da (data not shown). The greater sensitivity of E to zero filling (relative to h) is a specific example of the overall greater difficulty in measuring the phase. This can be understood in part by rearranging eq 1 to show that for a given oligomer

Ei ) mi - hi

(4)

where Ei is the residual mass for an oligomer of mass mi and degree of polymerization i. Differentiating eq 4 shows that ∂E/∂h ) -i. Since i will always be g1, the absolute uncertainty in E (|∂E|) will always be larger than that in h (|∂h|). Another source of uncertainty in interpreting φ should be considered. Recall that E includes the total end group () and adduct (k) mass. For systems with multiple E values (heterogeneous end groups and varying kinds of adducting ions), the phase will reflect a weighted average of all contributing values. This is a direct consequence of the superposition of functions of equal period and varying phase.22 Only if  and k are invariant, and if z and φ can be determined for each of two or more charge states (see below), should it be possible to separately determine  and k from differences between the φ (and derived E) values associated with each charge state. Fortunately, these uncertainties do not affect determination of h and z. Consideration of Multiple Charges. Figure 3 is an oversimplified example for many reasons, not the least of which is the unrealistic assumption of there being only a single charge state. This in turn introduces a major limitation to the utility of data like these: absent a priori knowledge of h or z, it would not be feasible to determine either separately from the transform of Figure 3c. This actually mirrors a general challenge in ES MSsincorporation of multiple charge carries with it a need to assess both m and z for a given ion. The problem can be solved elegantly (but expensively) by exploiting high resolution, so that z can be determined directly from the spacing of isotopic peaks. In many applications of ES, a simpler solution is derived from the observation of multiple charge states for a given analyte. As mentioned in the introduction, various “charge-stripping” routines have been devised to exploit charge multiplicity to enable separate determination of m and z. It was next considered whether FT might enable application of these routines to polymer ES data, where they would otherwise not be useful. Analytical Chemistry, Vol. 76, No. 1, January 1, 2004

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Figure 4. (a) Simulated electrospray mass spectrum of a hypothetical 40-kDa homopolymer with a 160-Da repeat unit, charge states of +15 to +22, and polydispersity of 1.002. (b) FT (solid line) of the data of (a) and Gaussian weighting (dashed line) used to determine the relative contributions of the various charge states in the simulation. The spectrum was zero-filled to 215 points prior to transformation.

Figure 4a results from superposition of distributions analogous to Figure 3a, calculated with charge varying from +15 to +22, and Gaussian weighted so that the +18 and +19 charge states are of approximately equal intensity, while intensities for the other charge states decrease smoothly to ∼12% (relative to the corresponding intensities in the +18 and +19 distributions). In generating f (x) for each charge state, p, x0, and b (eq 2) were scaled so that the distributions remained centered on the same mass (therefore differing m/z) and reflected the same polydispersity (a similar number of peaks above ∼1% relative abundance)

for each charge state; thus p(z) ) 160/(z); x0(z) ) 40 000/z; and b(z) ) 1845/z [b(z) was scaled so ∼70 peaks were above 1% relative abundance for a given charge state]. Although the resulting polymer envelope (Figure 4a) is considerably more complex than that of Figure 3a, the resulting FT of these data (zero filled to 215 points; Figure 4b) is still simple. Peaks are detected for eight charge states, as expected. Because there are multiple charge states, the problem of separately evaluating h and z is overdetermined, as it is in conventional ES of single analytes. Using the simplest charge-stripping algorithm2 (simultaneous solution for the two unknowns using pairs of peaks) provides seven independent estimates of h and z using the data from each peak with each of the other seven peaks; results for both z and h are in good agreement with expected values (Table 1). As seen by comparing the peaks in Figure 4b to the Guassian weighting applied to the various charge states (dashed line), the relative intensities of the peaks in Figure 4b reasonably reflect the simulated charge distributions (to within about (14% relative, worst case). The precision of the z estimates in Table 1 (one standard deviation of the seven estimates obtained using each peak) reflects both the Gaussian weightings of the distributions and the fact that a constant m/z sampling interval in Figure 4a results in more points per peak for the distributions of lower charge; the precision is therefore better for lower charge states. The multiplication of the most abundant charge state (z ) 18) with the maximum of the unresolved envelope in Figure 4a (∼2180 m/z) returns an approximate peak mass of ∼39 240 Da, in good agreement with the simulation value (40 000 Da). Table 1 also displays the results from phase calculations for each of the charge states. The precision and accuracy of the average E value (E h ) increase when n is increased from 15 to 17 (E h improves from -0.14 ( 8.81 to -0.02 ( 6.28). It should be noted that calculated E values for z ) 21 and 22 are much less accurate than the other E values. For these two peaks, E converges to inaccurate values as n f 20 (E ) 151.8 (-8.2) and 13 for z ) 21 and 22, respectively). The inaccuracy results in part from the overlap of the FT peaks, resulting in a shifted peak maximum. The effect is consistent with the greater uncertainty in E relative to h, described above. Consideration of Noise. In addition to the simplifying assumptions outlined above, the simulated data of Figures 3 and 4 differ

Table 1. Polymer Characteristics Estimated by FFT of a Simulated ES Mass Spectrum (Figure 4a) of a 40-kDa Homopolymer with a 160-Da Repeat Unit, Charge States of +15 to +22, and Polydispersity of 1.002

measd peak period (p)

expected peak period (p ) h/z)

calcd end group plus adduct mass (E; expected E ) 0)a

average calcd charge state (z)b

expected charge state (z)

average calcd monomer mass (h; expected h ) 160)b

7.279 7.620 8.001 8.426 8.890 9.415 10.003 10.672

7.273 7.619 8.000 8.421 8.889 9.412 10.000 10.667

10.3 142.9 (-17.1) 1.6 5.9 153.6 (-6.4) 3.1 155.4 (-4.6) 6.2

22.10 ( 0.12 21.03 ( 0.14 19.99 ( 0.10 19.00 ( 0.11 18.01 ( 0.08 16.99 ( 0.04 15.99 ( 0.03 14.98 ( 0.02

22 21 20 19 18 17 16 15

160.9 ( 0.9 160.2 ( 1.1 159.9 ( 0.8 160.1 ( 0.9 160.1 ( 0.7 160.0 ( 0.4 159.9 ( 0.3 159.9 ( 0.4

a Estimated from the phase (φ) using eq 3 and the estimated value of h (average from column 6). Negative values are included when the calculated value exceeds half the expected h value and can be interpreted to represent ionization by loss of an ion (i.e., k < 0; see text). As always for polymer mass spectra, a measured E value may differ from the “true” one by (gh, where g is an integer. b Average and standard deviation of values obtained by pairing the indicated peak maximum with each of the other seven peak maximums in the transform (see text).

132 Analytical Chemistry, Vol. 76, No. 1, January 1, 2004

Figure 5. Simulated mass spectra analogous to Figure 4a, but with addition of random noise to give base peak signal-to-noise ratios of approximately (a) 5, (c) 10, and (e) 20. Parts b, d, and f are the Fourier transforms of the adjoining spectra, after zero-filling to 215 points. Part f includes insets which have been smoothed (four-point Savitsky-Golay), magnified by 25 times, and offset in order to show the peaks attributable to z ) 15 and 22.

from the experimental spectra of Figure 1 in that the latter are subject to the noise that inevitably affects real data. To test the effects of noise on the ability of the FFT algorithm to derive useful information from the spectrum, random noise was added to the data of Figure 4a in order to generate simulated spectra wherein the signal-to-noise ratio (S/N) for the base peak was about 5, 10, or 20. For simplicity, the peak-to-peak noise amplitude was fixed at the level calculated for the base peak; thus, the S/N was less for all other values of m/z. Since mass spectra are often shot noise limited (N ∝ xS), this approach probably overestimates the effects of noise. The resulting “noisy” spectra and corresponding transforms are shown in Figure 5. For the lowest S/N ratio (Figure 5a and b), only six of the eight charge states are readily discernible above the background in the FT, and it is difficult to discern the position of the peaks that are evident. Application of a four-point Savitsky-Golay smooth to the transform facilitates peak localization, but the precision and accuracy of the average z and h values (calculated as above) are relatively poor (Table 2). Values from the weak peak at p ∼ 10.25 are particularly suspect. Removing these improves the precision and accuracy of the other values;

the average h value improves from 149.1 ( 6.8 to 155.5 ( 2.4 (Table 2). While still inaccurate (recall that hsimulted ) 160), this is reasonably good performance for such a low S/N. As evident from the rest of Figure 5 and the other data in Table 2, the accuracy and precision improve as expected with increasing S/N. Though barely discernible, all eight charge states can be identified in the FT of the S/N 20 data (Figure 5f). For best accuracy and precision of the derived monomer mass and chargestate values, it would appear that S/N g 20 should be targeted. For accurate end group calculations, a higher S/N is necessary. This is not surprising in light of the sensitivity of E to the factors noted above. Finally, it is noteworthy that all of the transforms in Figures 4 and 5 indicate that the most abundant charge state is z ) 18. Multiplication of this value times the m/z at the peak of the unresolved envelope in the corresponding untransformed mass spectra gives estimates of the nominal sample molecular weight within 1.9% of the correct value, even with a S/N ratio of only 5. Experimental Data. Moving beyond simulated data, Figure 6a presents a negative ion electrospray spectrum of a solution of Analytical Chemistry, Vol. 76, No. 1, January 1, 2004

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Table 2. Polymer Characteristics Estimated by FFT of Simulated ES Mass Spectra (Figure 5) of a 40-kDa Homopolymer with a 160-Da Repeat Unit, Charge States of +15 to +22, Polydispersity of 1.002, and the Indicated Base Peak S/N

S/N 5

5e

10

20

measd peak period (p)a

calcd end group plus adduct mass (E; expected E ) 0)b

average calcd charge state (z)c

expected charge state (z)

average calcd monomer mass (h; expected h ) 160)c

estimated monomer massd

7.578 7.982 8.426 8.868 9.429 10.250 7.578 7.982 8.426 8.868 9.429 7.629 8.024 8.437 8.901 9.413 10.005 7.261 7.603 8.022 8.418 8.895 9.406 10.025 10.645

83.0 (-66.1) 47.6 6.2 48.9 51.2 94.7 (-54.4) 86.6 (-68.9) 49.7 6.5 51.0 53.4 46.0 101.3 (-59.9) 58.4 50.8 152.7 (-8.5) 16.5 68.1 68.5 96.4 (-63.3) 125.6 (-34.1) 22.0 121.0 (-38.7) 86.7 (-73.0) 53.3

19.96 ( 0.57 19.08 ( 0.75 18.32 ( 1.19 17.27 ( 1.59 15.61 ( 1.78 13.28 ( 1.14 20.15 ( 0.41 19.33 ( 0.58 18.68 ( 1.01 17.88 ( 0.93 16.39 ( 0.42 20.87 ( 0.32 20.11 ( 0.45 19.19 ( 0.20 18.19 ( 0.15 17.20 ( 0.20 16.08 ( 0.12 21.80 ( 0.36 20.61 ( 0.68 19.94 ( 1.02 19.03 ( 0.57 17.98 ( 0.35 17.00 ( 0.41 15.90 ( 0.61 15.28 ( 0.40

21 20 19 18 17 16 21 20 19 18 17 21 20 19 18 17 16 22 21 20 19 18 17 16 15

151.3 ( 4.3 152.3 ( 6.0 154.4 ( 10.0 153.2 ( 14.1 147.2 ( 16.8 136.1 ( 11.7 152.7 ( 3.1 154.3 ( 4.6 157.4 ( 8.5 158.6 ( 8.2 154.5 ( 4.0 159.2 ( 2.4 161.4 ( 3.6 161.9 ( 1.7 162.0 ( 1.3 161.9 ( 1.9 160.9 ( 1.2 158.3 ( 2.6 156.7 ( 5.2 160.0 ( 8.2 160.2 ( 4.8 159.9 ( 3.1 159.9 ( 3.9 159.4 ( 6.1 162.7 ( 4.3

149.1 ( 6.8

155.5 ( 2.4

161.2 ( 1.1

159.7 ( 1.7

a Expected values for each charge state are listed in Table 1. b Estimated from the phase (φ) using eq 3 and the estimated value of h (from column 7). Negative values are included when the calculated value exceeds half the expected h value and can be interpreted to represent ionization by loss of an ion (i.e., k < 0; see text). As always for polymer mass spectra, a measured E value may differ from the “true” one by (gh, where g is an integer. c Average and standard deviation of values obtained by pairing the indicated peak maximum with each of the other four to seven peak maximums in the transform (see text). d Average and standard deviation of individual values in the previous column. e Omitting the weak peak at p ) 10.250.

sodium poly(styrenesulfonate) of average molecular weight 4600. The observed polymer-related peaks are only ∼8% as intense as the most intense solvent-related background peaks at low m/z (not shown). To achieve a S/N of ∼20 at the polymer envelope maximum required ∼700 5-s scans over the range 100-1400 m/z. The unusual polymodal structure of the envelope resulted from an rf-only ion optical lens installed when the instrument was upgraded to use the “Z source”; in the current context, this extra noise source poses an additional challenge for deconvolution. The results of FFT analysis of the portion of Figure 6a between m/z 280 and 750 (omitting low-mass background and solvent peaks) are shown in Figure 6b and summarized at the top of Table 3. Using methods described above, the peaks at the right of Figure 6b are assignable to the 8th-13th charge states (calculated z values are all within one standard deviation of an integer) for material of h ) 203.7 ( 4.2 (within experimental error of 206.2 Da, the average mass of the sodiated monomer repeat unit). The small apparent underestimation of the monomer mass may reflect partial substitution of hydrogen (from the protic solvents) for sodium at some sites within the polymer chain. This would be consistent with the prominent features in the lower region (periods of 1-5 m/z) of Figure 6b; these peaks correspond to z ) 7-13 and h ) 22.5 ( 0.1, possibly reflecting the H-for-Na exchange. In an attempt to minimize such exchange, 200 µM NaOH was added to the sample and the mass spectrum was reacquired (Figure 6c); the FT from the alkaline sample is shown in Figure 6d, and the results are included in Table 3. The low-period peaks 134 Analytical Chemistry, Vol. 76, No. 1, January 1, 2004

are reduced to near the noise level, and the resolution of the other peaks is improved. The resulting monomer mass is now estimated to be 205.54 ( 3.67 Da, closer to the expected 206.2, and consistent with suppression of the exchange. As a final test for the effects of mixed hydrogen and sodium adduction, the sodium ions were removed by ion exchange chromatography and hydrogen incorporation was maximized by addition of 200 µM H2SO4. The resulting spectrum and its FT are shown in Figure 6e and f, respectively. The presence of lower charge states (z ) 5-13; Table 3) relative to Figure 6b is consistent with the expected protonation and with the general predictions of “wrong-way-round” ES MS.25,26 The estimated monomer mass is 183.96 ( 1.43, within experimental error of the value expected for the average mass of the protonated (instead of sodiated) monomer (184.2 Da). Multiplication of the most abundant charge state (z ) 9 for Figure 6b and f; z ) 11 for Figure 6d) times the maximum of the unresolved polymer envelope in the corresponding untransformed spectrum (m/z ∼430 ( 8, for all cases) results in a peak molecular weight of ∼3900-4700, in reasonable agreement with the nominal sample molecular weights (4600 for the sodiated polymer and 4000 for the protonated form). As noted above, the total residual (end group plus adduct) mass (E) of the polymer can be estimated from the phase shift data; the end group mass can then be estimated by subtracting (25) Mansoori, B. A.; Volmer, D. A.; Boyd, R. K. Rapid Commun. Mass Spectrom. 1997, 11, 1120-1130. (26) Zhou, S.; Cook, K. D. J. Am. Soc. Mass Spectrom. 2000, 11, 961-966.

Figure 6. (a) Polymer envelope from the negative ion electrospray mass spectrum of a 10 µM solution of sodium poly(styrenesulfonate) in methanol/water (50:50 v/v). (b) FT of the data from m/z 280-750 in (a). (c) Polymer envelope from the ES mass spectrum of a poly(styrenesulfonate) sample made basic by addition of 200 µM NaOH. (d) FT of the data from m/z 280 to 750 in (c). (e) Polymer envelope from the ES mass spectrum of a poly(styrenesulfonate) sample ion exchanged to remove sodium then acidified by addition of 200 µM H2SO4. (f) FT of the data from m/z 280 to 1000 in (e). Sufficient zero-valued points were added before the first experimental data point to bring the initial m/z value to 0, and then additional zero-valued points were added following the last experimental point so that the total number of points ) 2.15 In each spectrum, Bp connotes the absolute intensity of the maximum of the polymer envelope.

kz from E. It is reasonable to assume that k ) -23 for the alkaline sample, and k ) -1 for the acidic sample. Using these values gives combined end group masses j ) 159.2 ( 47.7 and 48.2 ( 16.8 (averages from data for various z values) for the basic and acidic samples, respectively (Table 3). The numbers are relatively imprecise and do not agree with one another within experimental error. This may indicate that, even for these samples, there are mixed adducts present. If one assumes that this is the case for the original sample, the adduct ion mass (k) could be considered to be a weighted average of sodium and proton loss, in the same proportion as that needed to generate h ) 203.7. Using such an average (k ) -20.9) gives an end group mass  ) 118.9 ( 70.1 for the original sample. This is even less precise than the other two values but is within experimental error of them. The combined end group mass () for these samples is reported by the manufacturer to be 58 Da (n-butyl + H). It may be significant that the data for the acidic sample come closest to

reasonable agreement with this value. This sample gave the highest absolute signal level; as such, it may come closest to the S/N > 20 condition proposed above. It also has the lowest charge state and, therefore, the most points per dalton, given the constant number of points per m/z; what appears to be excess noise in Figure 6e (compared with a and c) is apparently real spectral structure. While the agreement with the “true” value of  is encouraging, the uncertainties associated with phase measurements for data of low S/N preclude a definitive conclusion here. CONCLUSIONS Fourier transformation of unresolved or partially resolved polymer envelopes obtained by electrospray mass spectrometry clearly shows promise for providing information about monomer mass, charge distribution, and (with normal caveats concerning sampling and analyzer bias) average sample mass, even with relatively low S/N. Data quality must be higher to secure useful Analytical Chemistry, Vol. 76, No. 1, January 1, 2004

135

Table 3. Polymer Characteristics Estimated by FFT of an Experimental ES Mass spectrum of a Poly(styrenesulfonate) Sample, Treated as Indicated in Column 1 polymer sample original

original with 200 µM NaOH

ion exchanged with 200 µM H2SO4

measd peak period (p)

calcd end group mass ()a

est end group mass (j)b

av calcd charge state (z)c

av calcd monomer mass (h)c

est monomer mass (hh )b

15.724 16.903 18.609 20.284 22.537 25.500 14.806 15.846 17.189 18.782 20.698 22.790 25.676 29.282 13.989 15.251 16.626 18.273 20.178 22.790 26.004 30.274 36.221

44.5 188.6 (-15.1) 16.4 164.3 (-39.4) 149.1 (-54.6) 150.8 (-52.9) 26.9 191.3 (-14.2) 183.6 (-21.6) 177.8 (-27.7) 166.4 (-39.1) 118.7 (-86.8) 114.2 (-91.3) 89.5 43.3 69.1 74.5 58.9 39.6 49.4 44.6 32.1 22.6

118.9 ( 70.1

13.13 ( 0.20 11.69 ( 0.58 11.14 ( 0.93 10.22 ( 0.60 9.02 ( 0.35 7.84 ( 0.21 14.17 ( 0.18 12.89 ( 0.15 11.91 ( 0.19 10.96 ( 0.25 10.07 ( 0.45 9.16 ( 0.47 7.96 ( 0.40 6.64 ( 0.26 12.91 ( 0.16 12.12 ( 0.07 11.13 ( 0.10 10.16 ( 0.19 9.13 ( 0.30 8.03 ( 0.14 7.07 ( 0.06 6.08 ( 0.04 5.08 ( 0.05

206.5 197.7 207.5 207.4 203.3 199.9 209.7 204.4 204.8 205.8 208.4 208.8 204.3 198.2 180.7 184.8 185.1 185.7 184.3 183.2 183.8 183.9 184.1

203.7 ( 4.2

133.5 ( 57.0

48.2 ( 16.8

205.5 ( 3.7

184.0 ( 1.4

a Estimated from the phase (φ) using eq 3 and the estimated value of h (from column 7), and assuming k ) -20.9 for the original sample, -23 for the basic sample, and -1 for the acidic sample (see text). Negative  values are included when the calculated value exceeds half the expected h value and may result if the true value lies within experimental error of zero. As always for polymer mass spectra, a measured  (or E) value may differ from the “true” one by (gh, where g is an integer. b Average and standard deviation of individual values in the previous column. c Average and standard deviation of values obtained by pairing the indicated peak maximum with each of the other peak maximums in the transform (see text).

(average) end group masses from phase data. There are also fundamental limits to the polymer molecular weights that may be interpreted by this method; if the envelope degenerates to a true continuum, information will not be recoverable. Conversely, higher resolution should extend the molecular weight range accessible. Of course, if the resolution is adequate to baselineresolve oligomer peaks (as in Figure 1a and b), autocorrelation methods reportedly provide better results.21 Several extensions of this work are currently under investigation. Preliminary work indicates that the method can work with data from a time-of-flight analyzer, provided that the data are first linearized to contain a constant number of data points per m/z (by excluding data points as needed). More importantly, we are investigating the utility of these methods to determine the monomer ratio for mixtures of homopolymers as well as for copolymers. For the latter case, the results of Figure 6a and b indicate that small differences in monomer mass may result in

136 Analytical Chemistry, Vol. 76, No. 1, January 1, 2004

averaging rather than resolution. It will be of interest to determine what mass differencessif anyscan be resolved to provide simultaneous analysis. ACKNOWLEDGMENT Support for this work was provided by the University of Tennessee Measurement and Control Engineering Center (an NSF Industry/University Cooperative Research Center), and by the National Science Foundation (Grant EEC-9634522). The assistance of John Bartmess (University of Tennessee) and Scott Campbell (Sierra Analytics) is gratefully acknowledged.

Received for review July 19, 2003. Accepted October 8, 2003. AC0348266