Fitting COSAC Mass Spectral Results Using Non-Negative Least

Article Cite This: ACS Earth Space Chem. XXXX, XXX, XXX−XXX

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Fitting Cometary Sampling and Composition Mass Spectral Results Using Non-negative Least Squares: Reducing Detection Ambiguity for In Situ Solar System Organic Compound Measurements Markus Meringer,† Chaitanya Giri,‡,§ and H. James Cleaves, II*,‡,∥,⊥

ACS Earth Space Chem. Downloaded from pubs.acs.org by UNIV STRASBOURG on 11/13/18. For personal use only.

†

Department of Atmospheric Processors, German Aerospace Center (DLR), Münchner Straße 20, 82234 Oberpfaffenhofen-Wessling, Germany ‡ Earth-Life Science Institute, Tokyo Institute of Technology, 2-12-1-IE-1 Ookayama, Meguro-ku, Tokyo 152-8550, Japan § Gateway House, Indian Council for Global Relations, 3rd Floor, Cecil Court, Colaba, Mumbai 400 005, India ∥ Institute for Advanced Study, 1 Einstein Drive, Princeton, New Jersey 08540, United States ⊥ Blue Marble Space Institute of Science, Seattle, Washington 98154, United States S Supporting Information *

ABSTRACT: The chemistry occurring in the universe generates a huge variety of organic compounds abiotically. Significant progress has been made in understanding the types and distributions of these compounds in various planetary, asteroidal, cometary, nebular, and molecular cloud environments. One of the most exciting recent discoveries was the detection of low-molecular-weight organic species native to the surface of comet 67P/ Churyumov−Gerasimenko by the cometary sampling and composition experiment that was aboard the Philae lander of the European Space Agency. The identities of these species were estimated using a simple handfitting method. Here, we use a more rigorous statistical method to fit the same data and find that there is some variance between results obtained using the two methods. This paper offers recommendations to improve the numerical methods for fitting of mass spectra, which would lead to more confident identification of ambiguous-mass compounds. Such methods may also help maximize the gains of future samplingdriven space missions, to Europa, Titan, Mars and its moons, comets, and asteroids, by filling in gaps in current scientific knowledge regarding electron impact mass spectra of ambiguous-mass compounds. KEYWORDS: cometary chemistry, COSAC, mass spectrometry, non-negative least squares, organic compounds, origins of life, solar system organic chemistry

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INTRODUCTION On November 12th, 2014, the European Space Agency (ESA) landed the Philae probe on the nucleus of comet 67P/ Churyumov−Gerasimenko. This lander contained an evolved gas analyzer/mass spectrometer named COSAC (short for cometary sampling and composition experiment). As a result of technical problems during the touch-down of Philae and an unanticipated landing position, only a few spectra could be recorded, with these unfortunately only in “sniffing” mode, i.e., without chromatographic compound separation. Furthermore, the low mass resolution (∼300) of COSAC gave inherent compound identification ambiguity, even over this low mass range, where the possible isomer space is relatively small. Thus, the spectra show superposed signals that could reasonably be attributed to multiple compounds. Goesmann et al.1 used an “Occam’s razor” approach to reduce the uncertainty in the identification of a set of 16 compounds, followed by manual fitting in order of decreasing mass starting from mass/charge ratio (m/z) 59 u/e. © XXXX American Chemical Society

Low-resolution mass spectra are inherently ambiguous, while such spectra may be almost useless for high-molecular-weight species identification, they are challenging for low-molecularweight species assignment, where there may be few possible assignments but where misassignment may lead to large confusion. Any given integer mass could represent various molecular formulas, isotopomers, or constitutional isomers and still fall within the accuracy of the measurement. This ambiguity can be resolved to a certain extent by taking the full electron impact mass spectra (EI-MS) fragmentation patterns of the candidate structures into account and fitting them to the measured spectrum. Such a fit has been proposed by Goesmann et al.1 Because this study used manually Received: Revised: Accepted: Published: A

August 27, 2018 October 17, 2018 October 23, 2018 October 23, 2018 DOI: 10.1021/acsearthspacechem.8b00122 ACS Earth Space Chem. XXXX, XXX, XXX−XXX

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ACS Earth and Space Chemistry executed peak fitting, it inherently left room for more objective and potentially more accurate interpretation. For example, in the fit proposed by Goesmann et al.,1 it is not clear how to proceed if there is more than one reference spectrum with a signal at a given considered mass. This occurs first with the detected peak at m/z 59. Within the set of 16 compounds, the National Institute of Standards and Technology (NIST) mass spectral database provides three reference spectra with the highest mass peaks at m/z 59, identified in that report as acetamide [molecular weight (MW) of 59], propanal, and acetone (MW of 58). There is presently no unambiguous way to determine which of these alternative identifications or combinations should be favored using the applied fitting procedure of Goesmann et al.1 Goesmann et al.1 state that their provided solution presents a very conservative fit. This means that overfitting was avoided wherever possible, even at the cost of potentially higher uncertainties. However, the manual fit fulfills no formal mathematical optimality criterion, for instance, minimizing the residual sum of squares. Finally, repeating such manual fitting for future tasks, including more complex measurement spectra and/or higher numbers of reference spectra, would be extremely tedious. It is important to have the greatest confidence possible in the identification of compounds in extraterrestrial samples. This is because extraterrestrial compounds formed at various times and locations in the universe are often assumed to “feed forward”, e.g., to serve as feedstocks for more complex chemistry that follows during subsequent processing in other environments (e.g., from interstellar ice grains to asteroids), and thus, the complexification of organics in the universe is assumed to follow some predictable chemical pathways. Such compounds are also implicated in the origins of life,2 and thus, it is of fundamental interest to understand their nature and mode of synthesis. If there is a direct inheritance between gas-phase chemistry occurring in protosolar disks, icy grain chemistry, cometary composition, asteroidal organic composition, and ultimately the delivery of organic compounds to primitive solar system solid bodies where life may originate,3,4 indefinite detections, especially in the most primitive materials, such as comets, can introduce “upstream” noise to models that can add significant error to the interpretation of “downstream” chemical processes. With these problems in mind, we herein attempt to show how a simple spectral fitting method may be usefully applied to future in situ MS measurements of solar system bodies.

A physical measurement cannot fulfill the mathematical equation Ax = b because of residuals introduced by factors, such as instrument imperfections, noise, etc. The standard approach5,6 to find precise spectral fitting solutions is to minimize the residual sum of squares (RSS), which can be written as ||Ax − b||2. This problem can be solved by an ordinary linear least squares (OLS) fit. To take the constraint of non-negative unknowns x ≥ 0 into account, one can use a non-negative least squares (NNLS) fit.7 NNLS minimizes a convex functional over a convex set, which guarantees the absence of multiple local minima (page 264 in ref 8). The numerical NNLS problem is a special case of the linear least squares problem with linear inequality constraints (page 371 in ref 9; see also S-1 of the Supporting Information); hence, its solution x is unique if A has full rank.10 Non-negativity constraints are frequently used in numerical analysis,11 and particularly in the context of EIMS, non-negative least squares fitting has already been applied by Kerber et al.12,13 An interface to Lawson’s and Hanson’s FORTRAN implementation is offered by the R package of the same name.14 We used this package to apply NNLS to the spectra of the 16 compounds listed in Table 1 by Goesmann et al.1 COSAC intensities and NIST reference spectra were imported from COSAC_Table_S_1.xlsx, which is part of the Supporting Information of the same publication. The data given there is consistent with COSAC_Table_S_2.xlsx of the same source. These tables include negative COSAC signals, which are caused by background subtraction. We keep these negative values for the NNLS fit (see S-4 of the Supporting Information) and do not introduce any peak weighting. The measurement spectrum was normalized to base peak intensity 1, and we considered only signals up to m/z 78 as indicated in COSAC_Table_S_2.xlsx. The original fit by Goessmann et al.1 and the NNLS fit were compared in terms of RSS, ratio of unexplained intensity (see S-2 of the Supporting Information), relative abundances (calculated compound concentrations xi normalized to have sum 1), and contributions of the reference spectra to the fitted spectra (see S-3 of the Supporting Information). We applied the same procedure to the compounds of Table B1 by Altwegg et al.15 and report results in S-5 of the Supporting Information.

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RESULTS AND DISCUSSION COSAC identified ∼14 organic molecular unit mass species over a mass range of 16−62. There are 75 possible organic, non-ionic, covalent molecular formulas based on C, H, N, and O over the mass range of 2−62,13,16 which represent several hundred valid structural isomers, some of which may not have been prepared, isolated, or measured to date. The NIST database contains ∼114 compounds with EI-MS spectra in this mass range, of which 102 are organic, uncharged, covalent molecules (see S-4 of the Supporting Information). There are also low-molecular-weight compounds that have been prepared, such as thioformaldehyde [detected in the Rosetta orbiter spectrometer for ion and neutral analysis (ROSINA) double-focusing mass spectrometer (DFMS) of Table 3 by Altwegg et al.15], that do not have an EI-MS spectra deposited in the NIST database, and there may be other relevant compounds similarly missing. Thus, any such peak fitting is only as good as the database from which it relies. NNLS finds a slightly better fit than Goesmann et al.1 for the 16 compounds listed in Table 1 of the same publication, with a

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METHODS We describe here a simple mathematical model that allows peak fitting for the measured spectrum with a well-known optimization procedure. Let a1, ..., an denote the reference spectra used for the fit, i.e., with n = 16, and aij denotes the intensity of reference spectrum i at m/z j, as given in Table S2 by Goesmann et al.1 Further let bj denote the measured intensity at m/z j. Under ideal conditions, the measured intensities can be written as sums, bj = x1aj1 + ... + xnajn, with some non-negative weights that can be considered as concentrations xi of compound i in the mass spectrometer. With A = (aij) being the matrix composed of the reference spectra as columns and b being the vector composed of the measured intensities, this can be written as a system of linear equations Ax = b. B

DOI: 10.1021/acsearthspacechem.8b00122 ACS Earth Space Chem. XXXX, XXX, XXX−XXX

Article

ACS Earth and Space Chemistry RSS value of 0.00207. Goesmann et al.1 did not explicitly mention the RSS of their fit, but it can be reconstructed from the column labeled “MS fraction” in Table 1 of their publication, giving a value of 0.00343. Correspondingly, we calculated the ratio of unexplained intensity of the measured spectrum, which is 10% of the total (positive) intensity for NNLS and 11% for the original fit. The matrix used for the fit has full rank; therefore, this is mathematically the unique solution of the NNLS problem. Figure 1 compares the

42 and 56 point to either missing molecules, incorrect reference spectra, or potential deficiencies in the measurement. Table 1 and Figure 2 show the relative abundances of assigned species obtained from the two fits. The column

Figure 2. Relative abundances of chemical compounds obtained from the original COSAC mass spectral fit1 and the NNLS fit. Error bars indicate the accuracy estimates of a factor of 2 given in the same publication.

Figure 1. Measurement (lines), original fit (closed circles), and NNLS fit (crosses). Negative intensities are caused by background subtraction.

labeled “original fit” in Table 1 is a copy of the column labeled “MS fraction” in Table 1 by Goesmann et al.1 The column labeled “NNLS fit” contains the calculated relative abundances of the NNLS fit. Most significantly, NNLS does not need ethylamine or glycolaldehyde for its better fitting (for these two compounds, the corresponding variables meet the boundary condition at zero with equality). Instead, acetone and CO are weighted as being relatively less abundant, while methane, isocyanic acid, acetaldehyde, and propanal are weighted significantly more. Otherwise, the two fits show

measured spectrum and the results of the fits. Altwegg et al.15 noted the poor fit for the peaks at m/z 29 and 15, which are only partly accounted for by the original fit. Using NNLS, we obtain a better fit than that offered by Goessmann et al.1 for these two masses. The fits at m/z 16 and 59 consequently become a bit worse. Beyond that, the fits are quite similar. The remaining discrepancies between measurement and fits at m/z

Table 1. Compounds, Formulas, Nominal Masses, Exact Monoisotopic Masses, and Relative Abundances of Measured Species Obtained from the Original and NNLS Fits compound

formula

nominal mass

exact monoisotopic mass

original fit

NNLS fit

methane water hydrogen cyanide carbon monoxide methylamine acetonitrile isocyanic acid acetaldehyde formamide ethylamine methyl isocyanate acetone propanal acetamide glycolaldehyde ethylene glycol

CH4 H2O HCN CO CH3NH2 CH3CN HNCO CH3CHO HCONH2 CH3CH2NH CH3NCO CH3COCH3 CH3CH2CHO CH3CONH2 HOCH2CHO HOCH2CH2OH

16 18 27 28 31 41 43 44 45 45 57 58 58 59 60 62

16.031300 18.010565 27.010899 27.994915 31.042199 41.026549 43.005813 44.026215 45.021463 45.057849 57.021463 58.041864 58.041864 59.037113 60.021129 62.036779

0.7 80.92 1.06 1.09 1.19 0.55 0.47 1.01 3.73 0.72 3.13 1.02 0.44 2.2 0.98 0.79

2.06 80.38 0.66 0.15 2.15 0.58 1.33 2.12 3.61 0 2.73 0.09 1.36 1.42 0 1.35

C


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ACS Earth and Space Chemistry

Figure 3. Heat maps showing the composition of the fitted spectrum by the reference spectra for the original fit by Goesman et al.1 in the top panel and for the NNLS fit on the bottom panel.

generally good agreement within the tolerances given by Goesmann et al.1 Figure 3 offers more insight into the composition of the fitted spectra. The colors of these heat maps indicate the relative contribution of the peaks of the reference spectra to the fit; e.g., the red entries for methyl isocyanate at m/z 54, 55, 56, and 57 indicate that the reference spectrum of methyl isocyanate is the only contributor for the fitted peak at these positions. On the other hand, e.g., m/z 58 indicates the reference spectra of methyl isocyanate, acetone, and propanal contribute. Ethylamine and glycolaldehyde do not contribute to the NNLS fit (bottom panel); hence, the corresponding rows are blank. We see that at m/z 15 and 29 many reference spectra contribute, and for such situations, an algorithmic approach based on solid mathematical foundations shows clear advantages compared to a manual fit. The differences of the two heat maps are depicted in Figure S1 of the Supporting Information. The importance of this analysis rests in the ways returned data are turned into chemical evolution models. In this case, there is great interest in understanding how organic molecules are generated and complexified in protoplanetary environments because these molecules may play a role in the origins of life. Below, we discuss implications for condensed-phase chemistry if it could be proven that glycolaldehyde and ethylamine are not part of the chemical composition of the comet.

Glycolaldehyde (GA) in particular plays many important roles in chemical evolution models for the origins of observed meteoritic organic complexity17 and models for the origins of life.18 GA is important as an initiator in the formose reaction (e.g., ref 19), which produces sugars, which are a chemicaldiversity-generating compound class in the combinatorial chemistry that may have led to the complexity observed in carbonaceous meteorites. Thus, if GA was not an abundant reactant, the organic chemical diversity observed in carbonaceous meteorites would need to have been achieved by other mechanisms, for example, by rearrangements induced by heat, thermal shocks, or radiolysis or potentially from thermally treated formamide, as has been proposed.20 In contrast, the possibility of ethylamine not being a major species in this comet has less profound implications. To date, it seems clear that, in most molecular series in carbonaceous meteorites where amines can be regarded as precursors, for example, in amino acids presumably generated by the Strecker mechanism,21,22 amino acids predominate over N-methyl amino acids, which, in turn, predominate over N-ethyl amino acids,23 a trend also observed in amines themselves.24 Thus, the lack (or low level) of ethylamine is concordant with these observations.

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CONCLUSION There may exist a link between organic compounds detected via radio-astronomy observations in presolar disks, which are D


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ACS Earth and Space Chemistry potentially reflective of the early accretional chemical history of our solar system, and those detected by in situ measurements in comets and asteroids, which are reflective of later stages in solar system formation. Using new telescopes, such as the Atacama Large Millimeter Array and the Square Kilometer Array, the former type of detection will be made in increasing detail; however, remote sensing analysis will be difficult for extrasolar planetary systems for the near future. Once such molecules condense into solid objects, they become spectroscopically opaque, and sending in situ probes is beyond current technology. Compounds detected in comets could be precursors for warmer, more complex chemistry occurring on asteroids, creating materials that could have been delivered to the early Earth. Such materials and their flows within a star system, if they follow a common chemical evolutionary pathway, may be universally important for the origins of life. Misinterpreting compound assignment in the most primitive types of solar system materials could impact such chemical models. Both Altwegg et al.15 and Goesmann et al.1 have made it clear that the interpretation from the contemporary in situ mass spectral measurements warrants further scrutiny. Although the mass spectrum obtained from COSAC is a remarkable achievement in itself, its ambiguous interpretation can further steer the explication of the higher order chemistry in unwarranted ways. This could happen as a result of measurement imprecision, low spectral resolution, or bootstrapping of low mass compounds through assumed synthesis pathways. Using NNLS, the consistency of various compound sets with the COSAC spectrum can be conveniently checked extremely quickly. Such candidate sets could be retrieved from other instruments on the same or future missions, derived from laboratory experiments, extracted from the literature, computationally obtained from prebiotic reaction network simulations, or just using one’s intuition. In principle, it is also possible to use NNLS to test complete small-molecule chemical structure spaces. In case corresponding reference spectra are not contained in the NIST MS library, ab initio calculation of EIMS25 could become an alternative to laboratory measurements. NNLS offers a rigorous method for evaluating lowresolution mass spectra of compound mixtures. Given the ambiguity in isobaric species in the upper region of this mass range and the incomplete coverage of possible isomer space in the NIST database, the reported abundances determined through both types of fitting may misrepresent the actual contents of such samples. Any method that can lower the ambiguity in structural assignment should be accepted as advances for in situ astrobiology robotic missions.

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6), differences in heat maps of Figure 3 (Figure S-1), relative abundances retrieved by NNLS fits with and without negative signals as described in section S-4 (Figure S-2), original fit and NNLS fit as described in section S-5 (Figure S-3), comparison of detailed results for the alternative fit as described in section S-5 (Table S-1), and relative abundances obtained from the original and the NNLS fits as described in section S-5 (Table S2) (PDF)

AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. ORCID

H. James Cleaves, II: 0000-0003-4101-0654 Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS This study was made possible by support from the Earth-Life Science Institute (ELSI) and the ELSI Origins Network (EON). EON is supported by a grant from the John Templeton Foundation. The opinions expressed in this publication are those of the authors and do not necessarily reflect the views of the John Templeton Foundation. The authors thank Debarpan Das for assistance with the graphical abstract, which is based on an artwork published by DLR (CCBY 3.0).

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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/acsearthspacechem.8b00122. Linear least squares problems with linear inequality constraints (S-1), residual sum of squares and ratio of unexplained intensity (S-2), composition of the fitted spectrum by the reference spectra (S-3), influence of negative peak intensities to the NNLS fit (S-4), NNLS fit for an alternative set of compounds (S-5), NIST MS database query for compound of nominal mass 2−62 (SE


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Fitting COSAC Mass Spectral Results Using Non-Negative Least

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