Natural molecules can be classified into two main groups according to their functions and how they are synthesized (Fig. 1). In living organisms, a genetic code initiates and controls the synthesis of functional, discrete molecules, which range in size from multienzyme complexes and molecular machines through mid-sized natural products to small molecules (e.g. NO). These molecules are often assigned to well-established distinct classes, such as proteins/peptides, carbohydrates, lipids, and (less structurally related), natural products and metabolites. Groups of these molecules frequently act together in regulatory networks [1–4] so as to enable critical life functions. Typical biofluids and tissues are very complex mixtures which can be resolved into defined molecular fractions using current high-performance separation technologies.

Fig. 1 Natural complex organic materials divide into either functional biomolecules which eventually derive from a genetic code or complex biogeochemical nonrepetitive materials which are formed according to the general constraints of thermodynamics and kinetics from geochemical or ultimately biogenic molecules. While biomaterials are amenable to successful separation into unambiguously defined molecular fractions, complex nonrepetitive materials cannot be purified in the conventional meaning of purity due to their extreme intricacy; in fact, the molecular signatures of these supermixtures often approach the limitations imposed by the laws of chemical binding. Improvements in the resolution and sensitivity of analytical techniques combined with the use of minimal (non)invasive sampling techniques have enabled environmental and living systems to be observed to a degree of molecular resolution that was considered unthinkable only a few years ago. A molecular-level understanding of biogeochemical and life processes implies a key role for de novo structural analysis, which depends on the combined use of separation technology hyphenated to organic structural spectroscopy and integrated mathematical data analysis. Analyses of supermixtures depend even more on the mathematical analysis of correlated data obtained from complementary molecular-level precision analytical methods. The formation of NOM on the Earth preceded the evolution of life; the binding of NOM-derived prebiotic molecules to borate contributed to the synthesis of ribose, a crucial precursor of nucleotides, in good yield [5]. Later on in the Earth’s history, coevolution occurred between prebiotic/abiotic molecules, NOM and primitive and higher forms of life. The near-continuum of binding sites available to ions and organic molecules acts to buffer against environmental and chemical extremes in the geo- and biosphere, which could damage life because of their potent reactivity. This key supportive role of (for example) natural organic matter (NOM) in life processes is sustained by strong interactions between biological and geochemical cycles (Fig. 2). Hence, plant and animal residues are key ingredients of NOM synthesis, while NOM itself, which defines the bioavailability of crucial organic and inorganic nutrients, is indispensable for the sustenance of the microbial life at the bottom of the food chain

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Fig. 2 Natural organic matter (NOM) continuously interacts with a broad range of terrestrial, limnic and marine ecosystems. Common to all of these environments are the fundamental molecular aspects of life, and an availability of extended mineral surfaces for interactions with and binding of NOM. The dynamic equilibrium of NOM generation and decomposition spans timescales of many different orders of magnitude (from microseconds to hundreds of thousands of years), and it results from a combined action of biotic and abiotic reactions. NOM may be intrinsically recalcitrant because of the chemical structures of its organic molecules; alternatively, strong NOM–mineral interactions could alter the reactivity of these organic molecules towards increased resistance to degradation. The physical protection of organic matter at interior mineral surfaces provides alternative pathways that enable the recalcitrance of NOM. Photochemical degradation, one of the most significant abiotic reactions of NOM, often results in small molecules like CO₂, which are mobile and are easily distributed within various ecosystems. Biomolecules derived from photosynthesis or otherwise originating from a genetic code are eventually decomposed according to the general laws and constraints of thermodynamics and kinetics (Fig. 1). Over very long timescales, the interactions of NOM with minerals at elevated temperatures result in the formation of geopolymers, like kerogen, coal, and oil shales. These ancient materials participate in bio- and geochemical cycling through natural and anthropogenic combustion and through weathering [6]

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Fig. 3 Hierarchical order of intricacy associated with the structural analysis of materials, in terms of polydispersity and molecular heterogeneity (see the main text). The structures (connectivities and stereochemistry) of monodisperse molecules are readily accessible (provided that sufficient amounts of the material are available) by organic structural spectroscopy [7–9]. Supramolecular structures [10–12] require an adequate definition of the covalently bonded molecules and of their noncovalent interactions [13–16]. The structural analysis of nonrepetitive complex unknowns, which feature substantial levels of both polydispersity and molecular heterogeneity [17, 18], is most demanding in terms of methodology and concepts [19–22]. Any highly resolved three-dimensional structure of a monodisperse biomolecule is based on a precise description of the unique chemical environment of any single atom [23, 24]. Currently, the molecular-level structural analysis of complex systems is primarily focused on covalent bond definition. Future high-quality structural analyses of these materials will have to assess both the (classes of) individual molecules and their interaction mechanisms [25]

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The fate of the second vast group of molecules in the bio- and geosphere is governed by the rather fundamental restraints of thermodynamics and kinetics (Figs. 1 and 2). In these intricate materials, the “classical” signatures of the (geogenic or ultimately biogenic) precursor molecules, like lipids, glycans and proteins, have been attenuated [26, 27], often beyond recognition, during a succession of biotic and abiotic (e.g. photo- and redox chemistry) reactions. Because of this loss of a biochemical signature, these materials can be designated nonrepetitive complex systems. The quantity of molecules in the Earth’s crust that can be attributed to these nonrepetitive complex materials, in the form of kerogens and natural organic matter (NOM) alone, exceeds the quantity of functional biomolecules by several orders of magnitude [28, 29]. Examples include freshwater, marine, and soil organic matter, kerogens and aerosols, among others. These materials typically exhibit an extremely complex array of chemical structures and interactions across a large range of size- and timescales, resulting in molecular signatures that reflect the fundamentals of chemical binding rather than those of their precursors. These novel signatures may in fact cover a sizable proportion of the theoretically feasible molecular composition space (Fig. 9). This extraordinary heterogeneity of molecularly diverse species renders these materials refractory and also implies a limited probability of detecting identical molecules [18]. This contrasts sharply with even the most complex mixtures of biomolecules extracted from any living organism, from which molecularly pure fractions can be readily obtained.

Given these unique features, nonrepetitive complex systems epitomize supermixtures. The purification of a supermixture would, in the ultimate sense, approach a molecule-by-molecule separation—a feat beyond our reach, both conceptually and practically. Therefore, these complex nonrepetitive systems are operationally defined according to their properties rather than according to their chemical structures, and their purification (in the conventional sense of the word) remains elusive [18].

While the analysis of complex biomolecules has advanced to the degree that it is possible to obtain well-resolved three-dimensional molecular structures and even meaningful descriptions of dynamics and interactions [30–35], the molecular-level precision analysis of complex nonrepetitive materials remains rather rudimentary in comparison [20, 36–40]. First of all, theoretically well-founded approaches to numerically describe the complex, polydisperse and nonstoichiometric characteristics of nonrepetitive unknowns are missing at present, limiting our understanding of molecular structures and any application of quantitative structure–activity relationships (QSAR) when modelling their properties. Novel approaches suitable for a quantitative description of various hierarchical levels of molecular organisation (e.g. elements, fragments, molecules) must be developed. Secondly, a meaningful molecular-level analysis of nonrepetitive systems—such as aerosols, natural organic matter and native cell extracts—obviously cannot rely on target analysis, as most of the chemical environments and linkages present are simply not known (Fig. 3).

Consequently, any comparative analysis of nonrepetitive unknowns with reference materials is very unlikely to provide satisfactory molecular resolution, because rather tiny variations in chemical binding may strongly and often unpredictably affect the properties commonly used for detection, such as retention times and spectral signatures. These fundamental restrictions that are intrinsic to comparative and target analysis are not easily circumvented and they necessitate an independent, spectroscopic “bottom-up” approach to the molecular-resolution characterisation of these complex unknowns.

The ¹³C NMR spectrum of Suwannee river fulvic acid (SuwFA) shown in Fig. 7 was acquired at the GSF with a Bruker (Bremen, Germany) AC 400 NMR spectrometer, operating at 100 MHz for ¹³C. FTICR mass spectra were acquired at Bruker’s facilities with a 9.4-T APEXq FT mass spectrometer (data in Fig. 9) and a 12-T APEXq FT mass spectrometer at the GSF (Fig. 8). Here, FTMS spectra were acquired with a time domain size of 1 MWord (Fig. 8a; Fig. 9, typical resolution 3 × 10⁵) or 4 MWord (Fig. 8b, typical resolution 7 × 10⁵). For Figs. 8a and 8b, elemental compositions were computed with the DataAnalysis software, version 3.4 (Bruker), using the following restrictions: C, H, N, O, unlimited; S, P, 0–5; H/C ratio < 3, mass error ≤ 0.5 ppm; observance of the nitrogen rule. Exactly one elemental formula was obtained for each peak. The elemental formulae of Fig. 9 were batch-calculated using a software tool written in-house, as described elsewhere [36].

Fig. 5 Characteristic resolutions (peak capacity: total range / half width [57]) of various separation technologies and organic structural spectroscopic methods (see the main text). This diagram represents a two-dimensional projection of the analytical volumetric pixel space—comprising NMR spectroscopy, mass spectrometry and separation technologies—that defines our current capacity to depict variance in complex systems with molecular resolution (see Fig. 12)

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The numbers of isomers, as displayed in Fig. 11, were calculated by constructive enumeration using the software MOLGEN (Department of Mathematics, University of Bayreuth, Bayreuth, Germany). For this computation [58], certain restrictions were applied in order to exclude structures that are mathematically possible but are not likely to occur in materials of biogeochemical origin; this means that there are (1) no peroxides; i.e. no –O–O– connectivities; (2) no triple bonds (–C≡C–); (3) no three- or four-membered rings; and (4) no carbon with cumulative double bonds (=C=). The ¹H and ¹³C NMR spectra of cholesterolacetate (section of ¹H NMR spectrum in Fig. 6, top panels) and 2-carboxypyrene (Fig. 6, middle panels) were computed with ACD software (ACD/HNMR and ACD/CNMR Predictor, v. 5.0); the mass spectral isotope peaks of Ciguatoxin C₆₀H₈₆O₁₉ (Fig. 6, middle panels) were computed with Bruker Compass FTMS software.

Fig. 6 The two most significant methods of organic structural spectroscopy, nuclear magnetic resonance (NMR) and FTICR mass spectrometry, are based on high-precision frequency measurements. The top panels illustrate NMR and FTICR MS for atomic and molecular processes. The precessions of atomic magnetic moments in molecules are defined by the chemical environment, and this means that NMR yields unsurpassed resolution of short-range molecular order (in noncrystalline materials, for which X-ray crystallography is not available). In FT mass spectrometry, the orbital frequencies of ions depend on their molecular masses. Mid-size molecules (see middle panels) provide information-rich signatures in NMR and only single peaks in mass spectra (under conditions of non-fragmentation), while complex non-repetitive materials (see bottom panels) produce low-resolution signatures in NMR because of extensive peak overlap. High FT mass spectra resolution is retained for complex molecules, however, because of the extensive peak capacity of the technique (see Fig. 5)

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The two most influential organic structural spectroscopic methods for the investigation of complex materials, which depend upon high-precision frequency measurements, are NMR spectroscopy and FTICR mass spectrometry (Table 1, Figs. 6, 7). In NMR, the precession frequencies of individual atomic nuclei in an external magnetic field B ₀ are influenced by their respective chemical surroundings; in FTICR mass spectrometry, the orbital frequencies of ions in an ion trap cell depend on the mass and charge of the molecule of interest [59]. Both methods are isotope-specific, and the combination of NMR and FTICR mass spectral data provides more useful spectral information on complex unknowns at the molecular level than any other spectroscopic method at present.

When studying typical organic molecules, NMR spectra provide more information-rich data than mass spectra, because any single atom within can produce an individual NMR signature (Figs. 6 and 7) [7, 60–62]. In the absence of fragmentation, the mass spectrum of any particular molecule will contain only a single peak (in conjunction with its corresponding isotopic pattern [63, 64]). NMR spectra of ever more complex materials will eventually become near featureless because of the extensive overlap between individual NMR resonances [65]; however, the significance of the information is maintained because of the quantification reliability and insightful relationships between NMR chemical shift and extended substructures (at least for the “small” NMR-active nuclei, e.g. ¹H, ¹³C, ¹⁵N, ³¹P, which represent the key players in organic structural spectroscopy) [66]. Mass spectrometry retains its supreme resolution for extremely complex systems [63, 67–70], but will eventually become limited by the inability of mass spectrometry to (easily) discriminate between isomers [71]. Hence, mass spectra will at best represent isomer-filtered projections of the entire structural space of molecules (see Figs. 7, 8, 9, 10, 11).

Fig. 7 Molecular-level resolution spectroscopic data represent projections of the vast total structural space of molecules, for which count estimates range from 10⁶⁰ to 10²⁰⁰ [72]. The complementarity of NMR spectroscopy and mass spectrometry for the spectral characterisation of intricate materials is caused by the entirely different atomic and molecular processes that these methods rely upon (Fig. 6). Mass spectra reflect the isomer-filtered complement of the entire space of molecular structures. The compositional space of molecules can be probed with ultrahigh-resolution FTICR mass spectroscopy, resulting in single peaks for molecules (in the absence of fragmentation). NMR spectra represent site- and isotope-specific projections of the molecular environments (the projected NMR spectrum given here shows a ¹³C NMR spectrum for an aquatic NOM). Accordingly, typical organic molecules exhibit single mass peaks (molecular ions given here: C₉H₉NO₃) and more elaborate NMR signatures (¹³C NMR data are shown here for C₉H₉NO₃; see also Fig. 6). Because these atomic and molecular signatures are not entirely orthogonal, the data provided by NMR and MS show correlations that can be used to reconstruct chemical structures by empirical and mathematical back-projection. In mixture analysis, separation offers a (near-)orthogonal means of expanding the two-dimensional spectroscopic projection area into a three-dimensional analytical volumetric pixel space (see Fig. 12). Following separation, molecules that often exhibit wide concentration variances in mixtures can be investigated by combined NMR/MS, with acquisition parameters specifically adapted in order to maintain the optimum dynamic range, which is necessary for good-quality spectra

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Fig. 8 FT mass spectral resolution and the C,H,O-compositional space (see the main text and Fig. 9)

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Fig. 9 Van Krevelen diagram (which illustrates the C,H,O-compositional space) for consolidated ESI, APPI, APCI positive and negative ions of Suwannee river fulvic acid (SuwFA) in the mass range 200–700 Da (see the main text and Fig. 8)

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Fig. 10 Elucidating mass spectra of complex materials requires advanced means of data analysis, such as van Krevelen diagrams, which are based upon assigned molecular formulae, and fragment- or molecule-specific Kendrick mass defect analyses [73]. Any dot in the van Krevelen diagram of a complex material represents a projection of the elemental ratios derived from assigned molecular formulae, irrespective of molecular mass. Accordingly, any of these dots could represent an intrinsic superposition of all feasible isomers from possibly different molecular compositions, sharing only their respective elemental ratios. The numbers of chemically reasonable isomers easily account for many millions of isomers seen for moderately sized molecules (a few hundred Daltons), even when only a few double bond equivalents and heteroatoms (e.g. oxygen) are present (see Fig. 11)

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Fig. 11 The relationship between the FTICR mass spectral intensity and the number of feasible isomers in complex materials. The distribution of (chemically relevant) C,H,O-isomer counts within the C,H,O-compositional space is visualized here in a van Krevelen diagram (left) for the eleven feasible molecular compositions C_nH_mO_q that have an IUPAC nominal mass of 178 Da (see the main text). These molecules are arranged into three series (series 1a–1c with three members; series 2a–2f with six members; series 3a–3b with two members) of isobaric molecules, which are related by a formal exchange of CH₄ against oxygen. For any molecular composition, the number of chemically relevant isomers is given in units of 10⁴. Carboxyl-rich alicyclic molecules (CRAM), which represent a complex mixture of molecules with near-absent olefinic and aromatic unsaturation, have recently been identified in marine organic matter [18], and they occupy an area of C,H,O-compositional space for which the largest number of feasible C,H,O-isomers is expected (see the main text), suggesting that the actual number of different molecules in the mass spectra of CRAM for any given mass may correlate with mass spectral intensity patterns. The availability of aromatic moieties in Suwannee river fulvic acid (SuwFA) also allows chemically relevant structures at lower H/C ratios (see the main text). The green circumfenced area denotes the van Krevelen compositional space of SuwFA, as provided in Fig. 9 (note that the SuwFA here represents consolidated positive and negative ion APCI+APPI+ESI FTICR mass spectra, as opposed to the negative ion ESI FTICR mass spectra given in the case of CRAM; see the main text). The panel on the right shows the C_nH_mO_q isomers computed for an IUPAC nominal mass of 178 Da in an intensity versus mass display (analogous to a mass spectrum), denoted according to series 1–3 (see the main text). This pattern resembles the clusters of peaks observed in good-quality FT mass spectra of NOM (see Fig. 6, bottom panels, and Fig. 8), suggesting that the intensities of the C,H,O-derived mass spectral peaks of NOM follow the number of chemically relevant C,H,O-isomers computed

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Molecular-level resolution spectroscopic data represent projections of the vast total structural space of molecules, for which count estimates range from 10⁶⁰ to 10²⁰⁰ [72]. The complementarity of NMR and mass spectrometry for the spectral characterisation of intricate materials is caused by the entirely different atomic and molecular processes these methods rely upon (Fig. 6).

Mass spectra reflect the isomer-filtered complement of the entire space of molecular structures. The compositional space of molecules can be probed with ultrahigh-resolution FTICR mass spectroscopy, resulting in single peaks for molecules (in the absence of fragmentation). Two-dimensional projections of the structural space, like van Krevelen diagrams and Kendrick mass defect analyses, are indispensable tools for the evaluation of mass spectra of complex materials (Figs. 8, 9, 10, 11) [73, 113, 114]. NMR spectra represent site- and isotope-specific projections of the molecular environments. Therefore, typical organic molecules exhibit single mass peaks (molecule ions) in mass spectra and more elaborate NMR signatures (Figs. 6 and 7). Because these atomic and molecular signatures are not entirely orthogonal, the data provided by NMR and MS exhibit correlations that can be used to reconstruct chemical structures by empirical and mathematical back-projection.

The NMR and mass spectral data can be acquired via direct hyphenation or in separate experiments [115–117]. In mixture analysis, separation offers a (near-)orthogonal means of expanding the two-dimensional spectroscopic projection area into a three-dimensional analytical volumetric pixel space (see Fig. 12). Following separation, molecules that often exhibit wide concentration variances in mixtures can be investigated by combined NMR/MS, with acquisition parameters specifically adapted to maintain the optimum dynamic range necessary for good quality spectra. Particularly in the case of mixture analysis, any joint mathematical evaluation of these correlated data will reveal hidden detail and will considerably enhance the resolution as well as the significance of molecular-level information (see also Figs. 4 and 12).

Fig. 12 The currently accessible discrete volumetric pixel (voxel) space for the characterisation of complex materials is in the range of 10^8–14 voxels. Its expansion is defined by the significant resolution of the complementary techniques of nuclear magnetic resonance (10^2–5 buckets, depicting the short-range order of molecules), ultrahigh-resolution FTICR mass spectrometry (10^4–5 buckets, depicting molecular masses and formulae of gas-phase ions) and high-performance separation (10^2–4 buckets, depicting both ions and molecules; this provides a way to validate NMR against MS data); see also Fig. 5 for even wider expansion. The various projections of this voxel space, like separation/MS, separation/NMR and NMR/MS, can be realised in the form of direct hyphenation [104, 115, 117–120] and via mathematical analysis [121, 122]

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FTICR mass spectra show supreme resolution, as indicated by the 12-T negative ionization ESI FT mass spectra of a barley extract (Fig. 8a) and IHSS Suwannee River Natural Organic Matter (International Humic Substances Society NOM; Fig. 8b). Here, C_nH_mO_q molecules contribute most to the total ion count. These molecules can be arranged into series, which are related by the formal exchange of CH₄ against oxygen. Figure 8c denotes the mass peaks corresponding to the 37 theoretically possible and chemically reasonable C,H,O-compositions depicted in Fig. 8d that have a nominal mass of 301 Da. Note that negative M–H⁺ ions (i.e. [M−H+e]⁻) are observed in the FTICR mass spectra (Fig. 8b), and the C,H,O-compositions of molecules M are denoted in Fig. 8c. M and M–H⁺ differ in mass by one hydrogen (1.007825032 Da) minus an electron (0.000548625 Da); in Fig. 8c this difference is decomposed into a mass shift of one (see the shift between the mass axes) and an additional small mass spacing Δm = 0.000233878 Da. The molecules in the barley extract exhibit mass peaks outside of the range accessible for any C,H,O-composition (dotted purple box in Fig. 8a), indicating the presence of additional heteroatoms (e.g. N, P, S) in these ions.

Figure 8d denotes a van Krevelen diagram of the 37 chemically reasonable C_nH_mO_q molecules, in which the 16 C,H,O-ions observed in Fig. 8b are highlighted. The number of peaks identified corresponds to a coverage of 43% of the entire C,H,O-compositional space. These ions occupy an area for which the largest number of feasible C,H,O-isomers is expected (see Fig. 11).

Molecularly intricate materials, like natural organic matter (NOM), exhibit molecular signatures approaching the theoretical limits defined by the laws of chemical binding. In Fig. 9, a van Krevelen diagram of Suwannee River fulvic acid (SuwFA) depicts the elemental ratios of C_nH_mO_q ions (the ions shown represent a consolidation of the ions obtained by ESI, APCI and APPI positive and negative ionization from 9.4-T FTICR mass spectra; unpublished data). The peaks observed in the negative/positive ionization mode only are coloured green/orange; peaks observed in both positive and negative modes are depicted in black. The lack of signatures from biochemical precursor molecules [123] indicates the considerable level of processing typical of NOM. Within a mass range of 200–700 Da and the given limits of the H/C and O/C ratios, the minimum consolidated number of individual C,H,O-molecular compositions (4270) represents a sizable fraction (23%) of the entire feasible compositional space of C_nH_mO_q molecules (18414 in total; small grey dots). To further appreciate the remarkable intricacy of natural organic matter, it should be noted that any dot in the van Krevelen diagrams of these complex materials represents a projection of the elemental ratios derived from assigned molecular formulae, irrespective of molecular mass. Hence, the dots in the van Krevelen diagrams can represent multiple molecular formulae (Figs. 10 and 11), while any identified molecular composition reflects an intrinsic superposition of all feasible isomers (Fig. 11). Considering typical molecular weights of several hundreds of Daltons in the mass spectra of NOM (Fig. 6, bottom panels), it is readily anticipated that the mass spectra of such systems represent simplified (e.g. isomer-filtered) projections of a still hugely more expansive structural space (Fig. 7).

For any exceedingly complex material, it is logical to postulate that many isomers will contribute to any given molecular formula. Analogously, the intensities of the mass spectral peaks, which superimpose all of the isomers present, will be a function of the abundances of these isomers in these materials and the ionization efficiency of each isomer under the given experimental conditions.

For molecules of a given mass composed of carbon, hydrogen, and oxygen, two major and independent trends are expected to define the number of feasible isomers. First, decreasing the H/C ratio from fully saturated molecules (C_nH_2n+2) means removing hydrogen atoms, which is equivalent to introducing double bonds or (ali)cyclic structures (double bond equivalents, DBEs). Molecules with large H/C ratios are structurally fairly uniform, consisting mainly of various branched chains of single bonds. Introducing large numbers of DBEs will lead to many new structures with double bonds and or (ali)cyclic structures in various positions. For an H/C ratio of close to one, on average two carbons carry one DBE, and the introduction of further DBEs will lead to a lack of single bonds. Hence, the maximum number of feasible C,H,O-isomers is expected to occur for intermediate numbers of DBEs in a molecule, because the occurrence of a DBE (which solely depends on the H/C ratio) enables double-bond displacement and the formation of (ali)cyclic structures, both of which greatly enlarge the number of feasible isomers. In contrast, only highly condensed structures can be assembled at very low H/C ratios [37], and this constraint severely diminishes the number of feasible C,H,O-isomers (if mathematically possible but chemically unlikely isomers are excluded; see Fig. 11).

Second, the insertion of oxygen into potentially any carbon–carbon (creating C–O–C units) or carbon–hydrogen bond (creating C–OH functionalities) will result in many more feasible isomers at low O/C ratios; in the presence of DBEs, “terminal” carbonyl derivatives (C=O) can also be constructed. At higher O/C ratios, however, further insertion of oxygen decreases the number of feasible isomers for two reasons: oxygen provides fewer (two) options for forming (single) bonds with other partners than carbon (four); in addition, the higher mass of oxygen (16 Da) compared with that of carbon (12 Da) decreases the total number of “heavy” atoms available for the construction of C_nH_mO_q molecules of a given mass.

These considerations imply that the number of feasible C,H,O-isomers for a given mass will reach maximum values at intermediate H/C and O/C ratios, and that these numbers will (sharply) decline at extreme (high and low) H/C and O/C ratios, respectively.

These dependencies are displayed in a van Krevelen diagram (Fig. 11), in which the numbers of chemically relevant isomers for any given molecular composition C_nH_mO_q of a single nominal IUPAC mass are provided. For any given nominal mass, the mathematically possible and chemically relevant structures composed solely of carbon, hydrogen and oxygen atoms can be constructively enumerated for each composition (molecular formula) [58]. By “chemically relevant isomers”, we mean all mathematically possible isomers (not counting stereoisomers) except for those containing O–O bonds, C≡C bonds, three- or four-membered rings, or =C= fragments (cumulated double bonds), which are not assumed to occur in the materials of interest (natural organic matter here). These data are displayed in the right panel of Fig. 11, where they are arranged according to actual mass.

For practical reasons, we have selected C_nH_mO_q compositions with a nominal IUPAC mass of 178, for which the number of isomers can be computed within a reasonable time on a desktop computer; within the given limits of H/C and O/C elemental ratios, eleven feasible C,H,O-molecules are found, which are grouped into three series of isobaric molecules, related by a formal exchange of CH₄ for oxygen (Fig. 11).

Series 1 represents highly unsaturated molecules in which the number of isomers declines sharply with decreasing H/C ratio. Series 2 presents the maximum number of isomers at intermediate H/C (and O/C) ratios and the decline in the number of isomers at both high and low H/C (and O/C) ratios, as anticipated (see above).

The maximum H/C ratio found for a series 2 molecule amounts to almost 1.7, and the corresponding molecule C₁₃H₂₂ (2a) features three DBEs, thereby allowing for a much larger array of unsaturation-related isomers than obtained for a fully saturated parent molecule. This is demonstrated by the variance in the isomer count when the fully saturated analogue C₁₃H₂₈ (184 Da, 802 isomers) is compared with the series 2 “endmember” C₁₃H₂₂ (2a; 178 Da, 1.7 × 10⁵ isomers); analogous relationships are found for the series 1 “endmember” C₁₄H₁₀ (1a; 178 Da, 5.3 × 10⁶ isomers) in comparison with its fully saturated parent molecule C₁₄H₃₀ (198 Da, 1858 isomers).

A considerable fraction of the 16.6-fold increase in the isomer count observed when comparing C₁₃H₂₂ (2a; three DBEs) and C₁₂H₁₈O (2b; four DBEs) results from the ability to produce novel isomers with singly bonded oxygen and those with a C=O bond (carbonyl derivative). The maximum number of isomers (~1.1 × 10⁷ each) is attained for the molecules C₁₁H₁₄O₂ (2c; five DBEs) and C₁₀H₁₀O₃ (2d; six DBEs), respectively. Further exchange of CH₄ against oxygen again sharply decreases the number of feasible isomers [by a factor of 5.5 when proceeding from C₁₀H₁₀O₃ (2d) to C₉H₆O₄ (2e), and by a factor of 78 when changing from C₉H₆O₄ (2e) to C₈H₂O₅ (2f)].

The series 3 molecules C₇H₁₄O₅ (3a) and C₆H₁₀O₆ (3b) feature rather limited numbers of isomers because of their large O/C ratios (see above). A comparison of C₈H₂O₅ (2f) and C₇H₁₄O₅ (3a) indicates that extreme hydrogen deficiency restricts the feasible number of isomers more severely than almost full saturation. Molecules C₁₄H₁₀ (1a; ten DBEs, 5.3 × 10⁶ isomers; series 1), C₁₀H₁₀O₃ (3b; six DBEs, 1.1 × 10⁷ isomers; series 2) and C₆H₁₀O₆ (3b; two DBEs, 6 × 10⁴ isomers; series 3) are all related by a formal exchange of four carbons for three oxygen atoms. The introduction of oxygen initially outweighs the decrease in the number of carbon atoms and DBEs available because of (i) the reduced severity of unsaturation and (ii) the availability of oxygen to construct isomers (see above). Upon the transition from C₁₀H₁₀O₃ (2d) to C₆H₁₀O₆ (3b), however, both the lesser ability of oxygen to participate in chemical bonding (two bonds for any oxygen instead of four for any carbon) and the decline in available DBEs lead to a drastic decrease in the number of accessible isomers.

In a highly processed and supposedly exceedingly complex material such as deep sea marine organic matter, most of the molecules of formula C_nH_mO_q will contain an intermediate amount of unsaturation and numerous oxygen atoms [18, 20]. This flexibility to generate a potentially huge number of isomers implies that (in the absence of severe ion suppression) mass spectral intensities should correlate roughly with the number of feasible isomers for any given molecular composition. Recently, carboxyl-rich alicyclic molecules (CRAM) have been identified as prominent constituents of marine (and possibly freshwater and terrestrial) organic matter [18]. CRAM likely represent highly processed products of ultimately terpenoid origin and are expected to represent an extremely complex mixture of molecules. Based on the molecules of formulae C_nH_mO_q and a recognition of FT mass spectral intensities, the CRAM that occur in deep ocean marine ultrafiltered organic matter comform mainly to the region inside the dotted ellipsoid in the van Krevelen diagram of Fig. 11, which appears to coincide with the maximum number of feasible C,H,O-isomers.

The availability of aromatic structures in terrestrially and freshwater-derived NOM, such as that in Suwannee river fulvic acid (SuwFA; Fig. 9), opens up the compositional space of chemically relevant NOM molecules (see above) to significantly lower H/C ratios than accessible solely on the basis of open-chain unsaturation (e.g. olefinic and carbonyl) and alicyclic double-bond equivalents (DBE). These dependencies are nicely illustrated by comparing the van Krevelen diagrams of marine ultrafiltered dissolved organic matter (UDOM) [18], a blackwater NOM [18, 124], and that of SuwFA (Figs. 9 and 11). While mass spectra of marine UDOM are dominated by carboxyl-rich alicyclic molecules (CRAM), composed mainly of carboxylic groups and alicyclic rings with only negligible aromatic and olefinic unsaturation [18], the significant terrestrial, aromatic-rich signature present in both blackwater NOM and SuwFA populates the compositional space with notably lower elemental H/C ratios than feasible in marine UDOM [18].

It should be noted that oxygen-depleted molecules of formula C_nH_m are less likely to be ionized in standard ESI FTICR mass spectra in comparison with oxygenated molecules of formula C_nH_mO_q. Carbohydrates, which are oxygen-rich, also are less efficiently ionized under standard ESI-FTICR mass spectral conditions than carboxyl-rich molecules like CRAM. CRAM therefore represent the most likely constituents of NOM to produce strong signals in ESI-FTICR mass spectra.

The compositional space of Suwannee river fulvic acid (SuwFA) given in Figs. 9 and 11 is derived from consolidated positive and negative ion FTICR mass spectra, obtained via APCI+APPI+ESI ionization modes, thereby facilitating the observation of oxygen-depleted molecules (Fig. 9).

The current capacity to describe complex materials at molecular resolution can be visualized in the form of an analytical space comprising individual volumetric pixels (voxels). The range of this discrete and quantized space is 10^8–14 voxels, as defined by the significant resolution of the complementary techniques of nuclear magnetic resonance (10^2–5 buckets, depicting the short-range order of molecules), ultrahigh-resolution FTICR mass spectrometry (10^4–5 buckets, depicting molecular masses and formulae of gas-phase ions) and high-performance separation (10^2–4 buckets, has the capacity to investigate both ions and molecules, and so provides a way to validate NMR against MS data).

An investigation of these correlated data is feasible at the level of the direct hyphenation of separation and spectroscopy [e.g. LC/NMR and LC or CE/MS; corresponding to the rear faces of the voxel space [119, 125–128]) and by means of statistical heterospectroscopy (SHY) [129, 130]; corresponding to the top face (or any two faces) of the voxel space]. Any joint mathematical analysis of these correlated data will enhance the effective resolution of the data and the significance of the molecular-level analysis of complex unknowns [119, 121, 129].

This voxel space can be readily expanded to higher dimensions by including complementary data, like those derived from genomic and proteomic analyses [84, 131–134] or by recognising selective chemical reaction products [135–140]. Degradative approaches to the characterisation of complex systems produce limited amounts of unambiguously identifiable small molecules but lose crucial linkage information. Soft and selective biochemical and chemical reactions like mild hydrolysis, reduction, oxidation and derivatisation [141, 142] of complex systems will often result in larger fragments with valuable positional and stereochemical information for the assessment of synthesis and degradation pathways.

The chemical transformation of functional groups with NMR- and MS-recognisable labels enables isotope-specific functional group analysis based on structural rather than behavioural characteristics [143, 144]. Information concerning stereochemistry and stable isotope composition will become more important when assessing the origins and diagenesis of complex natural materials. Any progress in the determination of position-specific stable isotope composition (e.g. by NMR and MS methods) will be useful for advancing this field. Physical and chemical fractionation will greatly assist in these studies; further miniaturisation will enhance separation capacity and thereby improve the resolution of the analytical voxel space (Figs. 5 and 12).

Integrated biomarker profiling approaches [145–147] with higher resolutions, significances and accuracies will substantially improve the quality and relevance of current systems biology approaches in the health and environmental sciences. The great progress made in the molecular-level characterisation of complex systems over the last few years and foreseeable improvements in nascent technology and concepts will lead to strong synergetic effects that will further advance our understanding of any complex natural and living system whose properties and functioning depend on both strong (covalent) and weak (noncovalent) interactions.