Mathematical tools in analytical mass spectrometry

Resolution-enhanced Kendrick mass defect analysis for improved mass spectrometry characterization of lignin

Lignin is a promising renewable source of valuable organic compounds and environmentally benign materials. However, its involvement in economic circulation and the creation of new biorefining technologies require an understanding of its chemical composition and structure. This problem can be overcome by applying mass spectrometry analytical techniques in combination with advanced chemometric methods for mass spectra processing. The present study is aimed at the development of mass defect filtering to characterize the chemical composition of lignin at the molecular level. This study introduces a novel approach involving resolution-enhanced Kendrick mass defect (REKMD) analysis for the processing of atmospheric pressure photoionization Orbitrap mass spectra of lignin. The set of priority Kendrick fractional base units was predefined in model experiments and provided a substantially expanding available mass defect range for the informative visualization of lignin mass spectra. The developed REKMD analysis strategy allowed to obtain the most complete data on all the homologous series typical of lignin and thus facilitated the interpretation and assignment of elemental compositions and structural formulas to oligomers detected in extremely complex mass spectra, including tandem ones. For the first time, the minor modifications (sulfation) of lignin obtained in ionic liquid-based biorefining processes were revealed.

Novel bioanalytical strategy using isotope pattern deconvolution and ICP-QMS for the study of iron incorporation in erythrocytes: An insight to better assessment

Iron is an essential element for human life and its nutritional status in the human body is directly linked to human health. More than 1015 atoms of iron per second are necessary for the maintenance of haemoglobin formation. To predict iron bioavailability three approaches are normally employed: (a) faecal recovery; (b) plasma appearance; and (c) erythrocyte incorporation (the most used). Isotope Pattern Deconvolution (IPD) is a mathematical tool that allows the isolation of distinct isotope signatures from mixtures of natural abundance and enriched tracers. In this work we propose a novel strategy to assess erythrocyte iron incorporation, based on the use of an iron stable isotope (57Fe) and the IPD concept. This strategy allows direct calculation of the exogenous concentration of 57Fe incorporated into RBCs after supplementation. In this way, to determine the mass of iron incorporated into erythrocytes, the unique prediction that must be made is the blood volume, estimate to reproduce the natural dilution of the tracer (57Fe) in the blood. This novel bioanalytical approach was applied for the measurements of iron incorporation and further iron absorption studies in humans, using a group of twelve healthy participants, that should be further evaluated for the assessment of other chemical elements that could be of health concerns and directly impact society.

Kendrick mass defect analysis - a tool for high-resolution Orbitrap mass spectrometry of native lignin

Lignin is the second most abundant biopolymer in nature and a promising renewable feedstock for the production of aromatic compounds, composite materials, sorbents, etc. Being a complex mixture of oligomeric molecules with an irregular structure, natural lignin is an extremely difficult object to study. Its molecular level characterization requires advanced analytical techniques among which atmospheric pressure photoionization Orbitrap mass spectrometry holds a promising place. In the present study, Kendrick mass defect (KMD) analysis was proposed to facilitate the visualization and interpretation of Orbitrap mass spectra of the biopolymer on an example of Siberian pine dioxane lignin preparation. The use of the typical guaiacylpropane structure C₁₀H₁₂O₄ as a Kendrick base unit made it possible to effectively identify oligomer series with different polymerization degrees and structurally related compounds, as well as to reliably determine the elemental compositions and structures of oligomers with high molecular weights (> 1 kDa). For the first time, KMD analysis was applied to the interpretation of the complex tandem mass spectra of lignin oligomers, rapid discrimination of the product ion series, and the establishment of the main collision-induced dissociation pathways. It was demonstrated that especially promising was the use of KMD filtering in the study of broadband fragmentation tandem mass spectra, which allows for the structural characterization of all oligomers with a particular degree of polymerization.

Contrastive Learning-Based Embedder for the Representation of Tandem Mass Spectra

Tandem mass spectrometry (MS/MS) shows great promise in the research of metabolomics, providing an abundance of information on compounds. Due to the rapid development of mass spectrometric techniques, a large number of MS/MS spectral data sets have been produced from different experimental environments. The massive data brings great challenges into the spectral analysis including compound identification and spectra clustering. The core challenge in MS/MS spectral analysis is how to describe a spectrum more quantitatively and effectively. Recently, emerging deep-learning-based technologies have brought new opportunities to handle this challenge in which high-quality descriptions of MS/MS spectra can be obtained. In this study, we propose a novel contrastive learning-based method for the representation of MS/MS spectra, called CLERMS, which is based on transformer architecture. Specifically, an optimized model architecture equipped with a sinusoidal embedder and a novel loss function composed of InfoNCE loss and MSE loss has been proposed for the attainment of good embedding from the peak information and the metadata. We evaluate our method using a GNPS data set, and the results demonstrate that the learned embedding can not only distinguish spectra from different compounds but also reveal the structural similarity between them. Additionally, the comparison between our method and other methods on the performance of compound identification and spectra clustering shows that our method can achieve significantly better results.

How machine learning can accelerate electrocatalysis discovery and optimization

Advances in machine learning (ML) provide the means to bypass bottlenecks in the discovery of new electrocatalysts using traditional approaches. In this review, we highlight the currently achieved work in ML-accelerated discovery and optimization of electrocatalysts via a tight collaboration between computational models and experiments. First, the applicability of available methods for constructing machine-learned potentials (MLPs), which provide accurate energies and forces for atomistic simulations, are discussed. Meanwhile, the current challenges for MLPs in the context of electrocatalysis are highlighted. Then, we review the recent progress in predicting catalytic activities using surrogate models, including microkinetic simulations and more global proxies thereof. Several typical applications of using ML to rationalize thermodynamic proxies and predict the adsorption and activation energies are also discussed. Next, recent developments of ML-assisted experiments for catalyst characterization, synthesis optimization and reaction condition optimization are illustrated. In particular, the applications in ML-enhanced spectra analysis and the use of ML to interpret experimental kinetic data are highlighted. Additionally, we also show how robotics are applied to high-throughput synthesis, characterization and testing of electrocatalysts to accelerate the materials exploration process and how this equipment can be assembled into self-driven laboratories.

MFAssignR: Molecular formula assignment software for ultrahigh resolution mass spectrometry analysis of environmental complex mixtures

Ultrahigh resolution mass spectrometry is widely used for nontargeted analysis of complex environmental and biological mixtures, such as dissolved organic matter, due to its unparalleled ability to provide accurate mass measurements. Accurate and efficient characterization of these mixtures is critical to being better able to evaluate their effect on human health and climate. This characterization requires accurate mass signals free from isobaric interferences, instrument noise, and mass measurement biases, allowing for molecular formula identification. To address this need, an open source post-processing pipeline for ultrahigh resolution mass spectra of environmental complex mixtures software was developed. MFAssignR contains functions that perform noise estimation, ¹³C and ³⁴S polyisotopic mass filtering, mass measurement recalibration, and molecular formula assignment as part of a consistent data processing environment. Novel applications of mass defect analysis were used in the functions for noise estimation and isotope pair identification. Using formula extensions, exact mass measurements are converted to unambiguous molecular formulas via data dependent pathways, reducing a priori decisions. Optional molecular formula ambiguity and multiple non-oxygen heteroatoms are provided for custom user applications, including isotopically labeled reactive species, halogen-containing species, or tandem ultrahigh resolution mass spectrometry. This represents uncommon flexibility for an open-source software package. To evaluate the performance of MFAssignR, it was used to characterize a sample of biomass burning influenced organic aerosol and the results were compared to those from other available methods of molecular formula assignment and noise estimation. The differences between the methods are described here. Overall, the inclusion of a full pipeline of data preparation functions and the data-dependent ambiguity reductions in MFAssignR render excellent results and make MFAssignR well-suited for the consistent and efficient analysis of environmental complex mixtures. MFAssignR is publicly available via GitHub.

Measured mass to stoichoimetric formula through exhaustive search

Electrospray ionisation has revolutionised mass spectrometry. Coupled to high mass resolution, it provides the stoichiometric formula of a lot of molecules in a mixture. The link between the mass spectrometry data and the chemical description relies on an interpretation of the measured masses. We present here the tools and tricks developed to exploit Orbitrap mass spectra. This piece of work focuses on the numerical method to assign a molecular formula to a measured mass. The problem is restrained to the solving of the Diophantine equation where the constant coefficients are stoichiometric groups. Peculiar case of a set of convenient groups is given with the chemical constraints it brings to the problem.

Two-dimensional decomposition of H-D exchange mass spectra of multicharged ions of biopolymers and their separation into components with independent H-D substitutions

The work is aimed at developing a numerical method for analysing mass spectra of deutero-substituted multicharged ions of biopolymers to determine contributions of components presumably corresponding to different biomolecule conformations. The two-dimensional decomposition of the H-D exchange mass spectra of two, three and four charged apamin ions with their separation suggests that the reaction of apamin ions with ND₃ molecules in the gas phase reveals hypothetically three different structural modifications of apamin ions. Usually for H-D exchange mass spectra, the presence of many resolvable protein structures was determined from measured distributions of peak intensities of ions with the same charge state. The method is new and has no published analogues. Graphical abstract.

On the Kendrick Mass Defect Plots of Multiply Charged Polymer Ions: Splits, Misalignments, and How to Correct Them

The Kendrick mass defect (KMD) analysis of multiply charged polymeric distributions has recently revealed a surprising isotopic split in their KMD plots-namely a 1/z difference between KMDs of isotopes of an oligomer at charge state z. Relying on the KMD analysis of actual and simulated distributions of poly(ethylene oxide) (PEO), the isotopic split is mathematically accounted for and found to go with an isotopic misalignment in certain cases. It is demonstrated that the divisibility (resp. indivisibility) of the nominal mass of the repeating unit (R) by z is the condition for homolog ions to line up horizontally (resp. misaligned obliquely) in a KMD plot. Computing KMDs using a fractional base unit R/z eventually corrects the misalignments for the associated charge state while using the least common multiple of all the charge states as the divisor realigns all the points at once. The isotopic split itself can be removed by using either a new charge-dependent KMD plot compatible with any fractional base unit or the remainders of KM (RKM) recently developed for low-resolution data all found to be linked in a unified theory. These original applications of the fractional base units and the RKM plots are of importance theoretically to satisfy the basics of a mass defect analysis and practically for a correct data handling of single stage and tandem mass spectra of multiply charged homo- and copolymers. Graphical Abstract ᅟ.

First Gut Instincts Are Always Right: The Resolution Required for a Mass Defect Analysis of Polymer Ions Can Be as Low as Oligomeric

Its recent adaptation to low-resolution mass spectra of polymers using fractional base units raises the question of the minimal resolution needed for a Kendrick mass defect (KMD) analysis. Intuiting an oligomeric resolution since the mass of a repeat unit is the sole value to be known, it is challenged by the relative failure of the KMD plots computed from an isotopically resolved matrix-assisted laser desorption ionization-time-of-flight (MALDI-TOF) mass spectrum to display clear alignments in the high mass range. Another procedure based on the remainders of Kendrick mass (RKMs) overcomes this pitfall with oligomers perfectly aligned in a new RKM plot. Despite a concomitant degradation of the resolving power and accuracy, with the example of MALDI-TOF/TOF mass spectra of a variety of homo- and copolymer ions, the RKM procedure still allows a rapid enumeration, assignment, and any further manipulation of all the product ion series in visual RKM plots. Successfully extended to the critical case of a MALDI mass spectrum recorded with a linear TOF analyzer allowing a bare oligomeric resolution, the RKM plot turns the distributions differing by their end-groups or adducted ion into clear horizontal lines. It eventually gives intuition its due by answering the original question: the minimal resolution required for a mass defect analysis can be as low as oligomeric with the appropriate formulas.

Toward chromium speciation in solids using wavelength dispersive X-ray fluorescence spectrometry Cr Kβ lines

The determination of chromium speciation in solid samples is critical for environmental and industrial purposes. Several analytical methods exist to perform such a determination either directly in solid state or liquid state after an extraction step, each of them having some limitations. In this study, the use of a high-resolution wavelength-dispersive X-ray fluorescence spectrometer to determine and quantify chromium species is investigated by looking at the differences in the Kβ transition profiles between Cr(0), Cr(III) and Cr(VI) compounds. Three different approaches were tested and compared to determine the Cr(VI) fraction of known mixtures: relative height and peak fitting using calibration mixtures, partial least square regression (PLS) of pure compounds, and principal component regression (PCR) of pure compounds. The accuracy of these methods was found to be about the same with an average relative error in the range of 15%. However, PLS and PCR can be easily implemented in an automated way contrary to peak fitting which can be sometimes perceived as analyst-dependant. Another advantage of using PLS and PCR is that information concerning the other oxidation states present in the sample can be retrieved. Finally, PLS and the peak height approach can be used up to 0.5% total chromium which make the XRF an alternative technique to X-ray induced photoelectron spectroscopy (XPS) for chromium speciation in solid state.

The stoichiometric transition from Zn6Cu1-metallothionein to Zn7-metallothionein underlies the up-regulation of metallothionein (MT) expression: quantitative analysis of MT-metal load in eye cells

We examined the profiling of gene expression of metallothioneins (MTs) in human tissues from cadaver eyes with microarray-based analysis. All MT1 isoforms, with the exception of MT1B, were abundantly expressed in lens and corneal tissue. Along with MT1B, MT4 was not detected in any tissues. Antibodies to MT1/2 labeled the corneal epithelial and endothelial cells, whereas MT3 label the retinal ganglion cells. We studied the effects of zinc and cytokines on the gene expression of MT isoforms in a corneal epithelial cell line (HCEsv). Zinc exerted an up-regulation of the expression of MT isoforms, and this effect was further potentiated in the presence of IL1α or TNFα. Zinc also elicited a strong down-regulation of the expression of inflammatory cytokines, and this effect was blocked in the presence of TNFα or IL1α. The concentration of MTs, bound zinc, and the metal stoichiometry of MTs in cultured HCEsv were determined by mass spectrometry. The total concentration of MTs was 0.24 ± 0.03 μM and, after 24 h of zinc exposure, increased to 0.96 ± 0.01 μM. The combination of zinc and IL1α further enhanced the level of MTs to 1.13 ± 0.03 μM. The average metal stoichiometry of MTs was Zn(6)Cu(1)-MT, and after exposure to the different treatments, it changed to Zn(7)-MT. Actinomycin D blocked transcription, and cycloheximide attenuated synthesis of MTs in the presence or absence of zinc, suggesting transcriptional regulation. Overall the data provide molecular and analytical evidence on the interplay between zinc, MTs, and proinflammatory cytokines in HCEsv cells, with potential implications on cell-based inflammatory eye diseases.

Higher-order mass defect analysis for mass spectra of complex organic mixtures

Higher-order mass defect analysis is introduced as a unique formula assignment and visualization method for the analysis of complex mass spectra. This approach is an extension of the concepts of Kendrick mass transformation widely used for identification of homologous compounds differing only by a number of base units (e.g., CH(2), H(2), O, CH(2)O, etc.) in complex mixtures. We present an iterative renormalization routine for defining higher-order homologous series and multidimensional clustering of mass spectral features. This approach greatly simplifies visualization of complex mass spectra and increases the number of chemical formulas that can be confidently assigned for given mass accuracy. The potential for using higher-order mass defects for data reduction and visualization is shown. Higher-order mass defect analysis is described and demonstrated through third-order analysis of a deisotoped high-resolution mass spectrum of crude oil containing nearly 13,000 peaks.

Kendrick-analogous network visualisation of ion cyclotron resonance Fourier transform mass spectra: improved options for the assignment of elemental compositions and the classification of organic molecular complexity

Here, we propose a novel computational and visual approach for the analysis of high field Fourier transform ion cyclotron resonance mass spectra (FTICR/MS) based on successive and multiple atomic and Kendrick analogous mass difference analyses. Compositional networks based on elemental compositions and functional networks based on selected functional groups equivalents enable improved assignment options of elemental composition and classification of organic complexity with tunable validation windows. The approach is demonstrated through the analysis of a 12T FTICR mass spectrum of an intricate water soluble extract of a secondary organic aerosol with a previously established abundance in CHNOS molecules.

Advances in structure elucidation of small molecules using mass spectrometry

The structural elucidation of small molecules using mass spectrometry plays an important role in modern life sciences and bioanalytical approaches. This review covers different soft and hard ionization techniques and figures of merit for modern mass spectrometers, such as mass resolving power, mass accuracy, isotopic abundance accuracy, accurate mass multiple-stage MS(n) capability, as well as hybrid mass spectrometric and orthogonal chromatographic approaches. The latter part discusses mass spectral data handling strategies, which includes background and noise subtraction, adduct formation and detection, charge state determination, accurate mass measurements, elemental composition determinations, and complex data-dependent setups with ion maps and ion trees. The importance of mass spectral library search algorithms for tandem mass spectra and multiple-stage MS(n) mass spectra as well as mass spectral tree libraries that combine multiple-stage mass spectra are outlined. The successive chapter discusses mass spectral fragmentation pathways, biotransformation reactions and drug metabolism studies, the mass spectral simulation and generation of in silico mass spectra, expert systems for mass spectral interpretation, and the use of computational chemistry to explain gas-phase phenomena. A single chapter discusses data handling for hyphenated approaches including mass spectral deconvolution for clean mass spectra, cheminformatics approaches and structure retention relationships, and retention index predictions for gas and liquid chromatography. The last section reviews the current state of electronic data sharing of mass spectra and discusses the importance of software development for the advancement of structure elucidation of small molecules. ELECTRONIC SUPPLEMENTARY MATERIAL: The online version of this article (doi:10.1007/s12566-010-0015-9) contains supplementary material, which is available to authorized users.

Computational mass spectrometry for metabolomics: identification of metabolites and small molecules

The identification of compounds from mass spectrometry (MS) data is still seen as a major bottleneck in the interpretation of MS data. This is particularly the case for the identification of small compounds such as metabolites, where until recently little progress has been made. Here we review the available approaches to annotation and identification of chemical compounds based on electrospray ionization (ESI-MS) data. The methods are not limited to metabolomics applications, but are applicable to any small compounds amenable to MS analysis. Starting with the definition of identification, we focus on the analysis of tandem mass and MS(n) spectra, which can provide a wealth of structural information. Searching in libraries of reference spectra provides the most reliable source of identification, especially if measured on comparable instruments. We review several choices for the distance functions. The identification without reference spectra is even more challenging, because it requires approaches to interpret tandem mass spectra with regard to the molecular structure. Both commercial and free tools are capable of mining general-purpose compound libraries, and identifying candidate compounds. The holy grail of computational mass spectrometry is the de novo deduction of structure hypotheses for compounds, where method development has only started thus far. In a case study, we apply several of the available methods to the three compounds, kaempferol, reserpine, and verapamil, and investigate whether this results in reliable identifications.

Total mass difference statistics algorithm: a new approach to identification of high-mass building blocks in electrospray ionization Fourier transform ion cyclotron mass spectrometry data of natural organic matter

The ultrahigh-resolution Fourier transform ion cyclotron resonance (FTICR) mass spectrum of natural organic matter (NOM) contains several thousand peaks with dozens of molecules matching the same nominal mass. Such a complexity poses a significant challenge for automatic data interpretation, in which the most difficult task is molecular formula assignment, especially in the case of heavy and/or multielement ions. In this study, a new universal algorithm for automatic treatment of FTICR mass spectra of NOM and humic substances based on total mass difference statistics (TMDS) has been developed and implemented. The algorithm enables a blind search for unknown building blocks (instead of a priori known ones) by revealing repetitive patterns present in spectra. In this respect, it differs from all previously developed approaches. This algorithm was implemented in designing FIRAN-software for fully automated analysis of mass data with high peak density. The specific feature of FIRAN is its ability to assign formulas to heavy and/or multielement molecules using "virtual elements" approach. To verify the approach, it was used for processing mass spectra of sodium polystyrene sulfonate (PSS, M(w) = 2200 Da) and polymethacrylate (PMA, M(w) = 3290 Da) which produce heavy multielement and multiply-charged ions. Application of TMDS identified unambiguously monomers present in the polymers consistent with their structure: C(8)H(7)SO(3)Na for PSS and C(4)H(6)O(2) for PMA. It also allowed unambiguous formula assignment to all multiply-charged peaks including the heaviest peak in PMA spectrum at mass 4025.6625 with charge state 6- (mass bias -0.33 ppm). Application of the TMDS-algorithm to processing data on the Suwannee River FA has proven its unique capacities in analysis of spectra with high peak density: it has not only identified the known small building blocks in the structure of FA such as CH(2), H(2), C(2)H(2)O, O but the heavier unit at 154.027 amu. The latter was identified for the first time and assigned a formula C(7)H(6)O(4) consistent with the structure of dihydroxyl-benzoic acids. The presence of these compounds in the structure of FA has so far been numerically suggested but never proven directly. It was concluded that application of the TMDS-algorithm opens new horizons in unfolding molecular complexity of NOM and other natural products.

Mass spectrometric characterization of naphthenic acids in environmental samples: a review

There is a growing need to develop mass spectrometric methods for the characterization of oil sands naphthenic acids (structural formulae described by C(n)H(2n+z)O(2) where n is the number of carbon atoms and "z" is referred to as the "hydrogen deficiency" and is equal to zero, or is a negative, even integer) present in environmental samples. This interest stems from the need to better understand their contribution to the total acid number of oil sands acids; along with assessing their toxicity in aquatic environments. Negative-ion electrospray ionization has emerged as the analytical technique of choice. For infusion samples, matrix effects are particularly evident for quantification in the presence of salts and co-elutants. However, such effects can be minimized for methods that employ chromatographic separation prior to mass spectrometry (MS) detection. There have been several advances for accurate identification of classes of naphthenic acid components that employ a range of MS hyphenated techniques. General trends measured for degradation of the NAs in the environment appear to be similar to those obtained with either low- or high-resolution MS. Future MS research will likely focus on (i) development of more reliable quantitative methods that use chromatography and internal standards, (ii) the utility of representative model naphthenic acids as surrogates for the complex NA mixtures, and (iii) development of congener-specific analysis of the principal toxic components.

Valence parity renders z(*)-type ions chemically distinct

Here we report that the odd electron z (*) -type ions formed by the electron-based peptide dissociation methods (electron capture or transfer, ECD or ETD) have distinctive chemical compositions from other common product ion types. Specifically, b-, c-, and y-type ions have an odd number of atoms with an odd valence (e.g., N and H), while z (*)-type ions contain an even number of atoms with an odd valence. This tenet, referred to as the valence parity rule, mandates that no c-type ion shall have the same chemical composition, and by extension mass, as a z (*) -type ion. By experiment we demonstrate that nearly half of all observed c- and z (*) -type product ions resulting from 226 ETD product ion spectra can be assigned to a single, correct, chemical composition and ion type by simple inspection of the m/ z peaks. The assignments provide (1) a platform to directly determine amino acid composition, (2) an input for database search algorithms, or (3) a basis for de novo sequence analysis.

High-precision frequency measurements: indispensable tools at the core of the molecular-level analysis of complex systems

This perspective article provides an assessment of the state-of-the-art in the molecular-resolution analysis of complex organic materials. These materials can be divided into biomolecules in complex mixtures (which are amenable to successful separation into unambiguously defined molecular fractions) and complex nonrepetitive materials (which cannot be purified in the conventional sense because they are even more intricate). Molecular-level analyses of these complex systems critically depend on the integrated use of high-performance separation, high-resolution organic structural spectroscopy and mathematical data treatment. At present, only high-precision frequency-derived data exhibit sufficient resolution to overcome the otherwise common and detrimental effects of intrinsic averaging, which deteriorate spectral resolution to the degree of bulk-level rather than molecular-resolution analysis. High-precision frequency measurements are integral to the two most influential organic structural spectroscopic methods for the investigation of complex materials-NMR spectroscopy (which provides unsurpassed detail on close-range molecular order) and FTICR mass spectrometry (which provides unrivalled resolution)-and they can be translated into isotope-specific molecular-resolution data of unprecedented significance and richness. The quality of this standalone de novo molecular-level resolution data is of unparalleled mechanistic relevance and is sufficient to fundamentally advance our understanding of the structures and functions of complex biomolecular mixtures and nonrepetitive complex materials, such as natural organic matter (NOM), aerosols, and soil, plant and microbial extracts, all of which are currently poorly amenable to meaningful target analysis. The discrete analytical volumetric pixel space that is presently available to describe complex systems (defined by NMR, FT mass spectrometry and separation technologies) is in the range of 10(8-14) voxels, and is therefore capable of providing the necessary detail for a meaningful molecular-level analysis of very complex mixtures. Nonrepetitive complex materials exhibit mass spectral signatures in which the signal intensity often follows the number of chemically feasible isomers. This suggests that even the most strongly resolved FTICR mass spectra of complex materials represent simplified (e.g. isomer-filtered) projections of structural space.