High Performance Quantification of Complex High Resolution Polymer

Letter Cite This: ACS Macro Lett. 2018, 7, 1443−1447

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High Performance Quantification of Complex High Resolution Polymer Mass Spectra Kevin De Bruycker, Tim Krappitz, and Christopher Barner-Kowollik* School of Chemistry, Physics and Mechanical Engineering, Queensland University of Technology (QUT), 2 George Street, Brisbane, QLD 4000, Australia

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S Supporting Information *

ABSTRACT: Modern soft ionization mass spectrometry provides chemical information on various polymers with unparalleled resolution and sensitivity. However, the interpretation of the resulting highly complex mass spectra is hampered by the sheer amount of contributing macromolecular species. For example, state-of-the-art reversible deactivation radical polymerization techniques, which are generally considered to be highly controlled, can still generate tens or even hundreds of species in a narrow mass window. Moreover, the multitude of species typically leads to partially overlapping isotopic patterns, further complicating the data evaluation. Herein, a rapid and powerful three-step methodical approach is introduced that enables the successful identification and quantification of the contributing species. The approach is subsequently implemented in “pyMacroMS”, a high performance algorithm that allows for ultrafast processing of high resolution polymer mass spectra with varying complexities. The power of our algorithm is demonstrated on the example of a photochemical atom transfer radical polymerization (photoATRP) of three monomers, ultimately leading to 908 identified species. pyMacroMS is available free of charge under a GNU General Public License v3.0.

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spectra that are inherently difficult to interpret. Indeed, the more complex the mixture, after preseparation via SEC, the higher the number of experimentally recorded signals and accompanying chance on isobaric overlap. This hampers a straightforward qualitative differentiation between signals originating from different species as well as their quantification in the mixture. For example, various macromolecular species with different end groups were identified in contemporary photoinduced ATRP (photoATRP) of methyl methacrylate in a previous study by our group,15 even though this polymerization technique allows for precisely controlled reaction conditions by tuning the photonic field parameters, generally resulting in a well-defined polymerization degree.16−18 Nevertheless, quantification of the different species based on a mass spectrum provides valuable information regarding the degree of control in the system, even though an experimental error may result from the ionization bias that is inherent to ESIMS.9,19 While the amount of unique species as a result of different end groups is still limited for a homopolymer, copolymers or terpolymers theoretically contain tens or hundreds of species, respectively, in an m/z range of merely 100 Da, which takes hours if not days to analyze manually. Therefore, the

oft ionization mass spectrometry has emerged as an indispensable technique for the detailed analysis of synthetic polymers, mainly because it yields chemical information at an unparalleled sensitivity compared to typical analytical techniques, e.g., NMR spectroscopy and conventional size exclusion chromatography (SEC).1−6 The obtained data include the exact molecular weight of both the repeating unit and the end groups formed during the polymerization reaction. However, the mass spectrometer effectively analyzes every macromolecular chain in the polymer, often resulting in complex spectra, especially in the case of copolymers.7,8 Nevertheless, using soft ionization techniques, such as matrix assisted laser desorption ionization (MALDI) and electrospray ionization (ESI), chain fragmentation can be largely suppressed, which strongly simplifies the recorded spectra while retaining the chemical information.9−11 Compared to MALDI, ESI is often referred to as the softer ionization technique, even preventing the fragmentation of polymers bearing labile end groups as obtained in reversible deactivation radical polymerizations.1,3,9,12,13 Furthermore, ESI can be readily combined online with a chromatographic separation technique, such as SEC, thereby significantly reducing the complexity of the polymer mixture prior to introduction in the mass spectrometer.7,14 In fact, SEC-ESI-MS allows us to deconvolute the overall mass spectrum by separately analyzing narrow fractions of the complete molecular weight distribution. Even with the aforementioned instrumental optimizations, a modern high resolution mass spectrometer typically produces © XXXX American Chemical Society

Received: October 18, 2018 Accepted: November 20, 2018

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DOI: 10.1021/acsmacrolett.8b00804 ACS Macro Lett. 2018, 7, 1443−1447

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Figure 1. Experimental high resolution ESI-MS spectrum (top) of a random terpolymer of poly[(methyl methacrylate)-co-(ethyl methacrylate)-co(butyl methacrylate)] obtained via photoATRP using ethyl α-bromoisobutyrate as initiator (experimental details can be found in the Supporting Information) in which 908 unique adduct ions were identified by the algorithm presented in this work. Automated quantification results in an accurate calculated spectrum (bottom), as evidenced by the respective insets. PMDETA: N,N,N′N″,N″-pentamethyldiethylenetriamine.

amounts of 908 unique ions, which account for 98% of the detected masses in a spectrum of poly[(methyl methacrylate)co-(ethyl methacrylate)-co-(butyl methacrylate)] (Figure 1), could be obtained in merely 14 min. Since any polymer can essentially be represented as a mixture of macromolecules, the analysis of a polymer mass spectrum starts with the generation of a molecule library. Each of these macromolecules is characterized by a certain combination of (co)monomers, which result in a total number of repeating units n, as well as a set of end groups. The number of unique molecules in this library is given by eq 1, with E the amount of possible end-groups, M the amount of comonomers, and n the total number of repeating units. Indeed, M different comonomers can be combined in C̅ M,n ways to obtain the same overall amount of repeating units n. Nevertheless, since C̅ 1,n = 1, eq 1 simplifies to the more intuitive eq 2 in case of a homopolymer. For example, a sample of poly(methyl methacrylate) (PMMA) obtained via photoATRP is expected to contain significant amounts of up to 9 different macromolecules (Figure 2a) for any number of methyl methacrylate units as a result of the possible end-group sets (E = 9).15 Next, each library entry is simply combined with a number of ions, such as a single Na+ for charge state 1, to obtain a list of adduct ions that can be detected in a mass spectrometer. Finally, an initial guess of the theoretical mass spectrum is produced by calculating the exact mass and the probability of all the isotopologues for each of these ions using IsoSpec, a fine structure isotope calculator for high resolution mass spectrometry.21 The result of this first stage is illustrated in Figure 2b, showing both the experimental spectrum and that of the molecule library for the aforementioned PMMA over a mass range of 100 Da, i.e., one repeating unit.

availability of algorithms that enable rapid data processing is of utmost importance to assist with the elucidation of complex polymer mixtures and the large amount of experimental information. Various programs are available that simulate high resolution isotopic patterns of (macro)molecular species20−24 or allow for the processing and analysis of experimental data in the field of bioinformatics, e.g., proteomics and metabolomics.25−29 However, to the best of our knowledge, only one example has been successfully applied for the analysis of polymer mass spectra.25 Moreover, this approach is limited to low resolution mass spectra of homopolymers, thereby strongly limiting the applicability for the fast quantification of complex high resolution polymer mass spectra. Herein, we demonstrate a methodical approach to identify and quantify various species in very complex high resolution polymer mass spectra, which we subsequently implemented in pyMacroMS, a computer algorithm that automates the complete process. The approach is based on the assumption that an isotopic distribution resulting from a mixture of compounds is a linear combination of the isotopic distributions of the individual compounds in the mixture.30 Consequently, a full combinatorial library of possible species is initially assembled on the basis of a list of (co)monomers and end groups, after which their isotopic distributions are generated, effectively yielding an initial guess of the theoretical spectrum. Second, the experimental masses are matched to the theoretical spectrum, allowing us to identify a set of species that can contribute to the experimental spectrum. Finally, quantification of these species is achieved via a linear regression with the experimental and theoretical ion abundances as dependent and independent variables, respectively. The versatility of this three-step approach is exemplified by providing an accurate analysis of polymer mass spectra of polymers obtained via photoATRP of methacrylic monomers with an unprecedented speed and accuracy. Moreover, the analysis is not hampered by overlapping isotopic envelopes since the complete isotopic pattern is used for linear regression, rather than a quantification based on the monoisotopic mass of each species. For example, relative

nmax

∑ n = nmin

nmax

ECM ̅ ,n =

∑ n = nmin

nmax

ECM + n − 1, n =

∑ n = nmin

E

(M + n − 1)! n! (M − 1)! (1)

E(nmax − nmin + 1) 1444

(2) DOI: 10.1021/acsmacrolett.8b00804 ACS Macro Lett. 2018, 7, 1443−1447

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Figure 2. (a) Main macromolecular species that are expected in a sample of PMMA obtained via photoATRP using ethyl α-bromoisobutyrate as initiator (experimental details can be found in the Supporting Information). (b) Overview of the three-step approach to identify and quantify the different species in a high resolution polymer mass spectrum of PMMA. Top to bottom: experimental spectrum, spectrum of the molecule library containing the main macromolecular species in the same relative amount, matched spectrum solely containing the library species that were identified in the experimental spectrum, and the final spectrum after correction for the relative quantities of each species.

isotopes were found to correspond to an experimental mass, as depicted in Figure 2b. As previously mentioned, the experimental spectrum is a linear combination of the isotopic patterns of the individual molecules in the sample. In other words, the sum of the peak intensities pm,l of the L molecules in the library at mass m, corrected for their relative amount al in the mixture, must yield the experimental peak intensity Pm at the corresponding mass (eq 3).30 The list of M experimental peaks with their contributing isotopologues, as identified by the matching algorithm, thus represents a system of linear equations that is equivalent to eq 4. In this equation, the experimental spectrum is the dependent variable whereas the (matched) theoretical peak intensities of the individual compounds are a set of independent variables. Consequently, in this final step, the relative amount of each identified molecule is calculated by determining the least-squares coefficients of a multivariable linear regression (Figure S2). Recalculating the matched spectrum, taking the obtained relative quantities of every macromolecule into account, resulted in a faithful reproduction of the experimental spectrum, as evidenced in Figure 2b. The complete experimental spectrum of the PMMA homopolymer was successfully reproduced by pyMacroMS in less than 5 s

As soon as the isotopic masses of the molecule library are generated, they can be used to identify the species that contribute to the experimental spectrum by matching each of the measured masses to one or more of these calculated values. This step proved to be of paramount importance for the successful quantification of the spectrum and required the introduction of two additional processing steps to yield a robust algorithm, while also limiting the amount of false positive matches. First, a threshold is introduced below which an experimental peak is considered as noise. Second, the isotopic peaks of each species that cannot be distinguished by the mass spectrometer are aggregated by calculating their probability-weighted average mass (Figure S1).31 In fact, IsoSpec generates an infinitely resolved spectrum for each of the species, while the spectral resolution is in reality always limited by the mass analyzer.21 For the actual matching of the isotopic peaks, a certain deviation between the experimental and theoretical masses must be allowed to account for inaccuracies in the recorded spectrum (Figure S1). Throughout this manuscript, a deviation of 5 ppm was considered tolerable. The result is a list of experimental peaks, each linked to a single isotopologue of one or more library molecules, allowing us to prune the library molecules of which none of the 1445

DOI: 10.1021/acsmacrolett.8b00804 ACS Macro Lett. 2018, 7, 1443−1447

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ACS Macro Letters

certain molecule is solely based on some of its least probable isotopes, the error on the corresponding calculated coefficient will be rather high. More specifically, when only one of these low-intensity isotopes is considered in the fitting, the coefficient can be freely adjusted to maximize the fit, yielding a list of relative quantities without a physical meaning. Nevertheless, the sum of the intensities of the matched M peaks for a single molecule (∑m = 1 pm , l ) is equal to the joint probability of the corresponding isotopologues and is thus a measure for the quality of the match. For example, the major isotopes are successfully matched for molecules with a joint probability close to 100%, while the molecule is most likely a mismatch, and should not be included in the regression, when this value is below a certain threshold. In the case of our highly complex photoATRP terpolymer, a threshold of 25% was found to effectively eliminate false positive matches without hampering the matching algorithm (Figure 3 and Figure S4b). This additional filter allowed for the faithful reproduction of the complete experimental mass spectrum, resulting from the successful identification and quantification of 908 unique adduct ions (some species were isobaric, Figure 1 and Table S2). In conclusion, our herein introduced algorithm pyMacroMS allows for the automated identification and quantification of macromolecular species in high resolution polymer mass spectra by matching the experimental peaks to a simulated molecule library that is based on a probable reaction mechanism, followed by a multivariable linear regression. Mismatched species are effectively filtered by ensuring that the experimental spectrum contains a minimum fraction of every theoretical isotopic envelope, while isobaric overlap is accounted for by considering complete isotopic patterns for the linear regression. Thus, accurate quantification of a myriad of species was achieved with an unprecedented speed, i.e., seconds up to a few minutes depending on the complexity of the mass spectrum. Consequently, the presented algorithm opens possibilities for high resolution mass spectrometry to be applied as a high throughput analytical technique for the elucidation of highly complex polymer mass spectra. pyMacroMS is open source, can easily be adapted for other polymers, and is available free of charge under a GNU General Public License v3.0 via the Python Package Index (pypi.org).

(Figure S3), yielding a list of 94 identified and quantified species (Table S1). L

Pm =

∑ pm,l al

(3)

l=1

P = pa with ÅÄÅ P ÑÉÑ ÅÅ 1 ÑÑ ÅÅ ÑÑ P = ÅÅÅÅ∂ ÑÑÑÑ ÅÅ ÑÑ ÅÅ P ÑÑ ÅÇÅ M ÑÖÑ

ÄÅ p É ÅÅ 1,1 μ p1, L ÑÑÑ ÅÅ ÑÑ ÅÅ ÑÑ Å ÑÑ p = ÅÅ∂ ∏ ∂ ÑÑ ÅÅ ÑÑ ÅÅ p Ñ μ p M ,L Ñ ÅÅÇ M ,1 ÑÖ

ÄÅ a ÉÑ ÅÅ 1 ÑÑ ÅÅ ÑÑ Å Ñ a = ÅÅÅ∂ ÑÑÑ ÅÅ ÑÑ ÅÅ aL ÑÑ ÅÇ ÑÖ

(4)

While the three-step protocol as described above was successfully applied to identify and quantify the different species for simple (homo)polymers with limited to no overlapping isotopic envelopes, a critical issue was discovered in the case of more complex polymers. For example, the calculated spectrum of a photoATRP terpolymer of methyl methacrylate, ethyl methacrylate, and butyl methacrylate does not resemble the experimental spectrum at all (Figure 3 and Figure S4a). This problem was found to be related to the inclusion of mismatched isotopic peaks with a low peak intensity in the linear regression. Indeed, if the fitting of a

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ASSOCIATED CONTENT

S Supporting Information *

The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acsmacrolett.8b00804.

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Figure 3. Experimental spectrum of poly[(methyl methacrylate)-co(ethyl methacrylate)-co-(butyl methacrylate)] obtained via photoATRP using ethyl α-bromoisobutyrate as initiator (top, experimental details can be found in the Supporting Information), the quantified spectrum without a threshold for the joint probability of contributing isotopologues (middle), and the quantified spectrum with a threshold of 25% for the joint probability of contributing isotopologues (bottom), highlighting the importance of a suitable threshold to eliminate false positive matches and to achieve a successful quantification.

Experimental details, supporting figures (various mass spectra), input/output of the algorithm executions, and a table of composition data of the identified species (PDF)

AUTHOR INFORMATION

Corresponding Author

*(C.B.-K.) E-mail: [email protected]. ORCID

Christopher Barner-Kowollik: 0000-0002-6745-0570 Notes

The authors declare no competing financial interest. 1446

DOI: 10.1021/acsmacrolett.8b00804 ACS Macro Lett. 2018, 7, 1443−1447

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ACKNOWLEDGMENTS

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REFERENCES

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C.B.-K. acknowledges funding from the Australian Research Council (ARC) in the form of a Laureate Fellowship (FL170100014) enabling his photochemical research program, as well as key support from the Queensland University of Technology (QUT). T.K. gratefully acknowledges funding by the Leopoldina Fellowship Programme, German National Academy of Sciences Leopoldina (LPDS 2017-05). The authors thank Tobias Nitsche for fruitful discussions.

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DOI: 10.1021/acsmacrolett.8b00804 ACS Macro Lett. 2018, 7, 1443−1447