Mass spectrometry

Abstract

There is provided a method of analysing isotopes of an element present in a compound of interest from a mass spectrum obtained by a Fourier transform mass spectrometer. The method comprises generating

Description

Field The invention relates to high-resolution mass spectrometry, in particular to the analysis of isotope ratios, isotopolog ratios and isotope / isotopolog clusters using Fourier transform mass spectrometry. Background As described in our US Patent No, 10,755,907, Fourier transform mass spectrometry often sees an analyte of interest undergo a separation step using established chromatographic techniques such as liquid or gas chromatography. This separation helps to reduce the complexity of the analyte sample. Subsequently, the analyte is ionized using established ionization techniques like matrix-assisted laser desorption / ionization (MALDI), electron ionization and atmospheric ionization including electrospray ionization (ESI), and the ions are directed into the Fourier transform mass spectrometer with ion optics. The ions may undergo further steps including isolation and / or fragmentation. Once inside the ion detector of the Fourier transform mass spectrometer, the ions may be trapped using an electric field, as in the case of the Orbitrap (TM) mass analyzer, or a combination of electric and magnetic fields, as in a Fourier transform ion cyclotron resonance mass spectrometer. Once trapped, resonant oscillations are induced in the ions. These oscillating ions generate a charge, known as the image charge, on the detector plates of the mass spectrometer. The resulting image current is measured by collecting a signal from the detector plates which is then amplified by a preamplifier, digitized, and recorded in the form of a transient. Generally, many transients are collected and processed together to derive a mass spectrum. Depending on the nature of the experiment, the interrogated analytes can generate a wide range of ionized species, spanning from individual atoms to complex biomolecules like proteins, as well as molecular complexes such as antibodies or viral particles. The natural variation in isotopes means that even molecular species with identical chemical (atomic) structures exist in multiple isotopic compositions. These different isotopic compositions are commonly referred to as isotopocules, isotopomers, isotopologs or isotopologues. An example is vanillin (4-Hydroxy-3-methoxybenzaldehyde) with a chemical composition CgHgOs. Carbon has multiple isotopes, including 12C and 13C, with natural abundances of 98.9% and 1.1% respectively. As a result, it is reasonable to assume the existence of vanillin molecules containing only the most abundant isotope, 12C (i.e. 12CgHgO3) as well as vanillin molecules carrying only 13C (13CgHgO3) or any mixture of them (13Cx12Cg. xHgOs) for that matter, where x is the number of 13C atoms. The relative abundances of a vanillin isotopologs can be calculated using the Bernoulli distribution and expressed in terms of probabilities (p): (8\ ) ■ p(13C)^ ■ (1 - p(13C))8 ^ xJ (1) Furthermore, hydrogen and oxygen also have stable isotopes pH, 2H, 160,17O and 18O). To account for this, eq.l can be generalized as: p(13Cx12C8.x1Hy2H8.y17Oz18Ow16O3.z-w) J-^0-(1-^0) + ().p(2Hy-(l-p(2H)) y (2) (C\ (C -z\ + ■ p(17O)z ■ ■ p(18O)w ■ (1 - p(17O) - p(wO^c-x~w \z) \ w ) This general concept can be expanded for molecules with any elemental composition. To date, the analysis of high-precision isotope ratios in complex molecules has involved a two-step process. First, the complex molecules are converted into smaller molecular moieties. Then, the isotope ratios of the resulting smaller molecules are analyzed using sector field mass spectrometers. Fourier transform mass spectrometers offer inherent advantages such as a high mass range and exceptional mass accuracy, enabling the measurement of isotope abundances in intact complex molecules, including those with higher masses. In these experiments, achieving the required analytical precision of the isotope ratios involves the averaging of multiple mass spectrometer scans of the same compound to increase the effective ion statistics. This process, known as signal averaging, entails collecting data over an extended period of time, which can range from minutes to hours, depending on the specific experiment and desired precision. In Fourier transform mass spectrometry, the length of the transient signal is proportional to the spectral peak resolution due to the nature of Fourier transformation. This means that increasing resolution results in slower scan rates which leads to a decrease in ion statistics (for the same scan time). To address this, the resolution is often reduced intentionally but this can result in some isotopolog peaks being unresolved. The non-integrable nature of the Fourier transform spectral peaks, where the summed intensity of unresolved or partially resolved peaks is not preserved, is known to lead to corrupted overall abundances of isotopolog spectral peaks. The precise evaluation of isotopic ratios in Fourier transform mass spectrometry spectra requires careful optimization of resolution settings which can be difficult. Returning to the example of vanillin, ionized as [M+H]+ ion, the monoisotopic peak consists of a single isotopolog composed of only light isotopes (12Cs1Hg16O3, MO), observed at 153.055 m / z. In contrast, the M+l peak at 154.05 m / z forms a cluster of isotopologs composed of heavier isotopes, including 13Ci12C71Hg16O3(13C), 12Cs1Hg17Oi16O2 (17O) and 12C82Hi1Hs16O3 (2H). This group of peaks is referred to in the art as an isotope cluster or isotopic fine structure. Additional isotope clusters can be observed at each consecent M+X, and these clusters have lower intensity and consist of multiple isotopologs. Resolving these clusters becomes increasingly difficult in the m / z domain due to their increasingly intricate fine isotopic structure. From eq. 2 above, it is evident that larger molecules generally exhibit higher overall abundances of heavier isotope clusters (M+l, M+2, and so on). These clusters contribute to a more complex and intricate fine isotopic structure, making it challenging to resolve them accurately in the m / z domain. This overall pattern of isotopic clusters in a compound is commonly referred to as its isotope pattern. FIG. 1 shows a portion of an exemplary mass spectrum collected from a vanillin sample at two different resolutions. The low-resolution (15k) mass spectrum shows only a single peak at m / z ~154.06 corresponding to the M+l isotopolog cluster and also a single peak at ~155.06 corresponding to the M+2 isotopolog cluster. However, the components of these peaks are resolved in the high-resolution (180k) mass spectrum. It can be seen that the M+l peak contains only a single significant component, the 13Ci isotopolog peak. While the M+l peak also has components arising from the 2Hi and 17Oi isotopologs, both have insignificant intensities. However, it can be seen that the M+2 isotopolog cluster has two components with significant intensities, the 18Oi and the 13C2 isotopologs (other isotopologs like 13Ci2Hi do not have a significant intensity that will adversely affect measuring the peak size of the isotopolog of interest). Isotopolog peaks may not be significant due to their intensity and / or m / z ratio relative to an isotopolog peak of interest (i.e. a more intense peak may not be significant if it is separated in m / z by a sufficient amount). Depending on the mass spectrometer resolution, significant interferences between significant peaks in an isotope cluster can occur, leading to overall suppression of the peak intensity and corruption of the spectral peak shapes, which can result in potential abundancy and m / z errors. The intensity errors arising from these spectral interferences are one of the major causes of inaccuracies in measuring isotope and isotopolog ratios, as well as isotope clusters / envelopes ratios. For example, when analyzing 18O and 34S isotopes in sulfate (HSO4j, the 34S and 18O peaks merge at lower resolutions causing inaccuracies in their respective intensities and hence intensity (abundance) ratios. The relative difference between the 34S / M0 and 18O / M0 ratios of two different sulfate materials may want to be determined, for example, as a 6 value in %o: 8 [%o] = Ratio Sample Ratio Reference - 1 * 1000 (3) However, merging of the peaks at low resolution settings (<10,000) can result in inaccuracies of up to 5 %o in the measured 6-value. The challenge of computationally deconvolving peaks positioned closer than the uncertainty limit of Fourier transformation is a well-known problem in Fourier transform mass spectrometry. Various methods have been proposed to address this problem, aiming to resolve the position and intensities of peaks beyond the limitations of Fourier transform uncertainty principle. These methods can be broadly categorized into two groups: those relying on prior information about the peak positions in the frequency (and therefore mass) domain, and those relying on blind deconvolution. An example from the first group is provided by US Patent No. 8,274,043. Examples of blind deconvolution include the filter diagonalization method, phased constrained spectral deconvolution method as also modified by the Prony method. While these methods can achieve super resolution, there are limitations to their utility in the field of Fourier transform mass spectrometry-based isotope ratio analysis. One limitation is that these methods assume the intensities of the peaks to be independent, which ignores a vital part of the information, i.e. the physical nature of the isotopes. Additionally, they exhibit heightened sensitivity to noise in the ranges beyond the Fourier transform uncertainty. Hence, these super resolution approaches in have limited utility. Summary According to a first aspect, the present invention resides in a method of analysing isotopes of an element present in a compound of interest from a mass spectrum obtained by a Fourier transform mass spectrometer. The method comprises generating simulated transients that would be measured in the mass spectrometer when measuring a sample of the compound of interest at one or more selected resolutions of the mass spectrometer. The simulated transients corresponding to samples of the compound of interest with different relative isotopic abundances. The method also comprises processing the simulated transients to produce respective simulated mass spectra data. The simulated mass spectra data are compared to theoretical mass spectra data to determine a correction to be applied to real mass spectra data to account for changes in isotopolog peak positions cause by interference between unresolved isotopolog peaks. Any of the mass spectra data mentioned herein may be a representation of one or more mass spectra, may be the data underlying such mass spectra (for example data relating signal intensities to m / z) or data derived from one or more mass spectra (for example the sizes of one or more peaks, of one or more ratios between peak sizes). Then, one or more corresponding real transients may be measured from a sample of the compound of interest using the mass spectrometer at the selected resolution. The one or more real transients may be processed in the same way as the simulated transients to produce real mass spectrum data. Put another way, this means that processing the simulated transients mimics the way that real transients are processed when creating real mass spectra data. A peak ratio is calculated from the real mass spectra data, for example a ratio of peak sizes such as peak heights or peak areas (that may or may not be measured relative to the background signal). Then, the correction may be applied to the calculated ratio to obtain a corrected ratio. The method may then comprise using the corrected ratio to determine information about the isotopic composition of the compound of interest. Several advantages are obtained using this particular method of correction through simulated mass spectra data. The method can be used to increase all or any of the parameters of isotope ratio analyses that are already being performed (i.e. parameters like precision, speed, and accuracy, when analysing flavors, drugs, amino acids, fatty acids, oxyanions,...). The method also extends the application space of the technique to the intact analysis of new compounds at higher mass ranges that were not accessible before due to limited mass resolution (Oligosaccharide, Lipids, Oligonucleotides, Peptides,...). The decreased mass resolution requirement for isotope ratio analysis makes such analysis more feasible and improves isotope ratio analysis generally. For example, in food applications (e.g. sugar analysis), it can decrease the time and sample amount required for the analysis 15-fold. This has a potential of increasing the throughput in terms of sample per unit of time (e.g. vanillin authentication analysis) with Fourier transform isotope ratio mass spectrometer dramatically and enables such spectrometry on the LC time scale enabling potential coupling of these techniques. This drastically expands its application space. Also, the need for manual labour intensive sample preparation is decreased. Optionally, generating the simulated transients comprises summing the contributions from isotopologs present in the compound of interest (either all or a subset of all isotopologs present), with the amplitude of each contribution being weighted according to the relative isotopic abundances of the isotopes present in that isotopolog. The method may include the contribution from the lightest isotopolog present in the compound of interest, although the method may use just heavier isotopologs. Analysing the corrected mass spectrum data to determine information about the isotopic composition of the compound of interest may comprise determining the ratio of heavier isotopes of an element to the lightest isotope of that element using the peak in the mass spectrum data arising from the lightest isotopolog present in the compound of interest. Generating the simulated transients may comprise including contributions from the plurality of isotopologs present in the compound of interest according to the natural isotopic abundances of the isotopes present in compound of interest. The simulated transients may be generated by varying the relative isotopic abundances of the isotopes present in compound of interest thereby producing different relative abundances of the isotopologs. Optionally, summing the contributions from the plurality of isotopologs present in the compound of interest comprises determining the frequency of the contribution according to the mass to charge ratio of the associated isotopolog. The method may further comprise determining first and second isotopes of an element of interest present in a compound to be analysed, wherein the first isotope is the lightest isotope and the second isotope is a heavier isotope. First and second isotopologs of interest that include the first isotope and second isotope respectively may be identified. The first isotopolog is the lightest isotopolog that generates a single, isolated peak when mass spectrum data are obtained by the mass spectrometer at the selected resolution. The method may further comprise identifying an isotopolog peak cluster containing a peak generated by the second isotopolog of interest when mass spectrum data are obtained by the mass spectrometer at the selected resolution, wherein the selected resolution is not sufficient to resolve the peak generated by the second isotopolog of interest from an interfering peak in the isotopolog peak cluster that interferes with the peak generated by the second isotopolog of interest. The interfering peak may be a peak that overlaps with the second isotopolog's peak and has sufficient size to affect the measured size of the second isotopolog's peak significantly. For example, peaks with over 5%, 10% or 20% of the size of the second isotopolog's peak may be considered to affect the measured size of the second isotopolog's peak significantly. Other peaks may be present in the cluster with sizes below these thresholds, but these peaks may be disregarded. The interfering isotopolog that contributes the interfering peak to the isotopolog peak cluster may be identified. The method may comprise identifying a linked isotopolog of the interfering isotopolog containing the same isotope as the interfering isotopolog, wherein that isotope is a heavier isotope of a further element present in the compound of interest, and the interfering isotopolog and linked isotopolog form a pair of an unresolvable linked isotopolog and a resolvable linked isotopolog. The mass to charge ratios of each isotopolog of the group of isotopologs may be determined based on the atomic masses of the isotopes present in each isotopolog. The group of isotopologs may comprise the first isotopolog of interest, the second isotopolog of interest, and the linked isotopologs. The frequency of the contribution that each isotopolog of the group of isotopologs will contribute to the transient signal may be determined. Then, the method may comprise calculating proportions of each isotopolog from (i) the natural abundances of the isotopes present in each isotopolog and (ii) generated abundances that vary around the natural abundances of the isotopes present in each isotopolog. Theoretical ratios of first and second isotopes may be determined from the calculated proportions. Simulated transients are generated by summing the contribution from each isotopolog of the group of isotopologs based on the calculated proportions of each isotopolog. The simulated transients are processed to produce simulated mass spectra data. Simulated ratios of first and second isotopes of interest are determined from the simulated mass spectra data. Also, the ratio of the heavier isotope of the further element to the lightest isotope of the further element are determined from the simulated mass spectra data by dividing the size of the peak produced by the resolvable linked isotopolog by the corresponding size of the peak produced by the lightest isotopolog. s noted elsewhere, the size of the peak may be the height or area of the peak, and may or may not be measured relative to the background signal. Then, the method may comprise determining the correction by determining a relationship between (i) the difference in (a) the ratio of the size of the isotopolog cluster peak to the size of the peak of the lightest isotopolog in the simulated mass spectra data and (b) the theoretical ratios of first and second isotopes, and (ii) the determined ratio of the heavier isotope to the lightest isotope of the further element. Optionally, the ratio of the first and second isotopes may be measured from the real mass spectrum data, and this ratio may be modified using the relationship. Thus, a correction may be applied to an isotope whose isotopolog peaks arising from heavy isotopes that cannot be resolved based on another isotope that has an isotopolog peak arising from a heavy isotope that can be resolved. The resolvable linked isotopolog may be an isotopolog with a single substitution of the isotope of the further element and the unresolvable linked isotopolog may be an isotopolog with multiple substitutions of the isotope of the further element. The unresolvable linked isotopolog may contain two 13C isotopes and the second isotopolog of interest be an isotopolog with a single 18O substitution. The compound to be analysed may comprise an organic molecule that contains carbon and oxygen, such as vanillin, PFAS, an organic alcohol, acid, aldehyde or ether. Also, the method may comprise determining isotopes of elements of interest present in a compound to be analysed. The isotopologs present in the compound of interest may be identified. The mass to charge ratios of the isotopologs maybe determined based on the atomic masses of the isotopes present in each isotopolog. The frequency of the contribution that each isotopolog of the group of isotopologs will contribute to the transient signal may be determined. The proportions of each isotopolog may be calculated from (i) the natural abundances of the isotopes present in each isotopolog and (ii) from generated abundances that vary around the natural abundances of the isotopes present in each isotopolog. For each isotope, the theoretical difference in isotopolog peak sizes from the calculated proportions for isotopologs containing varying abundances of that isotope may be determined. Simulated transients are generated by summing the contribution from each based on the calculated proportions of each isotopolog. The simulated transients may be processed to produce respective simulated mass spectra data. For each isotope, the method may comprise determining the simulated difference in isotopolog peak sizes from the simulated mass spectra data for the isotopologs used to calculate the theoretical difference in isotopolog peak sizes. Also, for each isotope, an intensity participation factor may be determined by comparing the simulated difference in isotopolog peak sizes to the theoretical difference for that isotope. Isotope ratios of each isotope may be determined based on the calculated proportions. For each isotopolog peak cluster, an equation may be formed linking the size of the peak to the isotope ratios and the intensity participation factors of the isotopes present in the isotopologs in that isotopolog peak cluster. The method may comprise measuring the ratio of the peak sizes of each isotopolog peak cluster to the peak size of the lightest isotopolog peak using the real mass spectrum data. The measured ratio may be substituted into the equation for each isotopolog peak cluster. Then, the equations may be solved to determine corrected isotope ratios for the real mass spectrum data. This method may be useful where there are no resolvable isotopologs containing heavier isotopes that may otherwise serve as a reference. Optionally, at least two isotopologs have peaks in a peak cluster that interfere with each other, and the at least two isotopologs are isotopologs of an element with three or more different isotopes. Then, the method may use the relation between the intensities of the different isotopes to correct the interference. The three or more different isotopes may be oxygen isotopes and the interfering peaks may arise from a 17O-substituted isotopolog and a 18O isotopolog. Hence, the related 17O and 18O peaks may be used to provide the correction. There is also provided a computer program comprising computer program instructions that, when executed by one or more computer processors, cause the one or more computer processors to perform any of the methods described above, and a computer readable medium having stored thereon such a computer program. There is also provided a computer system comprising one or more computer processors and computer memory having stored therein a computer program that, when executed by the one or more computer processors, cause the one or more computer processors to perform any of the methods described above. There is also provided a mass spectrometer comprising one or more computer processors and computer memory having stored therein a computer program that, when executed by the one or more computer processors, cause the one or more computer processors to perform any of the methods described above. Brief description of the drawings FIG. 1 shows individual isotope peak clusters observed in a mass spectrum of vanillin at 15k and 180k resolution; FIG. 2 is a schematic representation of an embodiment of a method of the present invention; FIG. 3 is a more detailed schematic representation of the embodiment of FIG. 2; FIG. 4 is schematic representation of one detailed embodiment of a method of the present invention; FIG. 5 is a plot of data extracted from simulated mass spectra and the linear fit that is used to obtain a correction; FIG. 6 shows 618O values for twenty one real vanillin samples measured at low resolution against the corresponding results obtained at high resolution; FIG. 7 shows the error on 613C created by differences in the 617O for acetate (C2H3O2) and the differences in 633S in methionine (C5H11NO2S); FIG. 8 shows individual isotope peak cluster observed in a mass spectrum of vanillin at 7.5k resolution, along with the participation of each isotopolog to the overall peak amplitude; and FIG. 9 is schematic representation of another detailed embodiment of a method of the present invention. Detailed description of the drawings The present invention addresses the problem of inaccuracies in isotope analysis due to the interference of unresolved peaks when using Fourier transform mass spectrometry. In some embodiments, the problem is addressed by simulating mass spectra of a compound of interest taking into account the different isotopologs that will be present, and using the knowledge from one resolvable isotopolog peak to correct the interference of other isotopolog peaks present in one or more isotopolog clusters. In other embodiments, the problem is addressed by simulating mass spectra of a compound of interest taking into account the different isotopologs that will be present, and using changes in peak sizes as different isotope abundances are simulated to correct isotopolog ratios determined from real mass spectra. To address the problem of inaccuracies in isotope analysis due to the interference of unresolved peaks, mass spectra of the compound of interest are simulated while varying different isotope abundances around their natural abundances, and as optionally repeated for multiple mass spectrometer resolutions. The peaks present in these mass spectra are used to determine ratios of isotopes which are, in turn, used to generate a calibration function that may be used as a correction in subsequent (real) mass spectrometry scans to correct the isotopic ratios obtained from the real mass spectra. This procedure can be performed for any compound to predict peak interferences at any resolution setting and additionally allows correction of interferences of any of the isotope ratios for the known compounds. This drastically increases the precision and accuracy of Fourier transform mass spectrometry ratio analysis. It also enables the analysis of isotopes ratio of large compounds that were inaccessible before as it allows to gain the abundances of each isotope from analysing clusters of unresolved isotopologs. A simulated mass spectrum of any compound of interest may be created from an artificial transient generated as described above by processing that artificial transient according to the same Fourier transform analysis performed by the mass spectrometer on real transients (i.e. by imitating the processing of experimentally-obtained transients by the mass spectrometer). Knowing the chemical formula of the compound of interest allows a list of isotopologs of the compound to be created. The mass to charge ratio of each isotopolog (m / z) can be calculated from the sum of the masses of the incorporated isotopes. Then, the mass to charge ratio of each isotopolog can be converted into the frequency (co) of the corresponding induced component in the transient as would be measured by a mass spectrometer: I ^isotopolog i (4) I ™ / Zisotopolog where k is a constant. The probability of each isotopolog (pisotopoiog) in a sample of the compound of interest can be calculated using Eq. 2 above that uses the natural relative abundance of each isotope present in each isotopolog. Hence pisotopoiog indicates the relative abundance of each isotopolog and, therefore, the amplitude of its component within the transient. The artificial transient (tran(t)) corresponding to the natural abundances of the constituent isotopes and isotopologs is then created by summing the harmonic contributions from each of the isotopologs. For example, the artificial transient (tran(t)) can be generated by summing up cosines with the frequency and amplitude of each of the isotopologs, weighted according to the abundance of each isotopolog: isotopologs tran(t) / Pisotopolog ' COS (2 ■ n ■ (^isotopolog ' Q (5) The artificial transients produced in these ways can be evaluated just like real transients measured by the mass spectrometer, which results in a simulated mass spectrum that incorporates the peak interferences that are also present in real data. Thus, ratios of isotopes may be determined from peak sizes in the artificial mass spectrum (e.g. peak heights or peak areas, which may be measured relative to the background (noise) signal level), e.g. by comparing the 13C M+l peak to the MO peak to obtain Routput13C. However, in unresolved isotopolog clusters, these ratios will be as inaccurate as the ratios obtained from real data due to the peak interferences. However, in this case we can determine theoretical ratios from the data used to generate the artificial transient and simulated mass spectrum. Specifically, the abundances (probabilities p) of the isotopes and isotopologs used to calculate the transients may be compared to derive theoretical ratios that would arise in the absence of mass spectrometer errors and peak interferences. For example, dividing PiSOtoPoiog of an isotopolog for one particular isotope by PiSOtoPoiog of the lowest mass isotope provides a theoretical ratio for that isotope, e.g. RinPut18O. In addition, theoretical ratios of pairs of heavier isotopes may be measured too from their respective values of PiSOtoPoiog- So, a calibration may be performed that can be used to correct ratios of isotopes measured from real mass spectra where the proportions of isotopologs may vary from that expected from the natural abundances of the constituent isotopes. To allow this, the calibration process may be repeated while changing the chemical formula, the relative abundances of the isotopologs (for example, as derived from the abundances of their constituent isotopes), or the mass spectrometer resolution. Hence, a set of simulated mass spectra are generated that encompasses different compounds or samples with different isotope or isotopolog ratios and different mass spectrometer resolutions. Corresponding theoretical ratios may be calculated for each simulated mass spectrum. Hence, full datasets are simulated that can be used to correct real mass spectra collected from different samples and at different mass spectrometer resolutions. In fact, these datasets may be used to pre-calibrate different types of corrections for data analysis of real mass spectra. Depending on how much information is known about the samples, and how many isotopologs and isotope clusters are analyzed and resolved, this can be utilized in different ways. Three different examples are described below. As a first example, a study of the isotopic ratio 18O / 16O in vanillin is considered. In the following, MO is used to identify the MO-isotopolog in vanillin, i.e. the [M+H]+ molecular ion without any heavy isotope substitution. It consists only of the lightest isotopes resulting in the chemical formula: 12C81Hg16O3.13Ci is used to denote the vanillin [M+H]+ molecular ion with a single 13C isotope substitution (13Ci-isotopolog). The chemical formula of this molecule is 13Ci12C71Hg16O3 with the short form 13Ci. The peak arising from this isotopolog appears in the M+l cluster where, as can be seen from FIG. 1, it is generally easy to resolve (and hence easy to measure accurately). 13C2 is used to denote the vanillin [M+H]+ molecular ion with two 13C isotope substitutions (13C2-isotopolog). The chemical formula of this molecule is ^Cz^Ce^g^Os, and it appears in the M+2 cluster along with the 18Oi isotopolog. The peaks arising from the 13C2 and 18Oi isotopologs are both significant and so interfere with each other, making their resolution and measurement difficult. Hence, vanillin is an example of a compound having two or more clusters of isotopolog peaks requiring analysis. The isotopolog ratio of interest (18O / 16O) is determined by a peak (18O) that appears in one of these clusters (M+2) where it is subject to interference from another isotopolog peak (13C2). In this example, we make use of the fact that the intensity / abundance of the interfering isotopolog peak (13C2) has a chemical (or physical or mathematical) relationship to a minimum of one other isotopolog peak from a different cluster that can be resolved. Consequently, the 13Ci and 13C2 isotopologs can serve as linked isotopologs, where a resolvable linked isotopolog (13Ci in this case) may be used to infer information regarding an unresolvable linked isotopolog (13C2 in this case). Knowledge of how the unresolvable linked isotopolog varies in the simulated mass spectra and, therefore, the ratio of that unresolvable linked isotopolog relative to the equivalent theoretical ratio may be used to determine information regarding the other unresolvable isotopolog (the isotopolog of interest) that is interfering with the unresolvable linked isotopolog. In this example, the unresolvable isotopolog of interest is the 18Oi isotopolog resident within the same M+2 isotopolog peak cluster as the 12C2 isotopolog peak. In the case of vanillin analysis at 7,500 or 15,000 resolution, the isotopolog ratio of interest (i8O / i6O or R18O for short) can be determined from the 18Oi-isotopolog peak which will be present in the M+2 peak cluster. As noted above, the M+2 cluster also contains the 13C2-isotopolog, and the18Oi-isotopolog and 13C2-isotopolog peaks interfere with each other. However, we know that the probability / abundance / intensity of the unresolvable linked isotopolog (13C2) is related to the intensity of the resolvable linked isotopolog (the isotopolog with a single 13C substitution - 13Ci). The 13Ci isotopolog is located in the M+l peak cluster where it is free of any significant interfering peaks. Hence, corrections can be made using regular data evaluation of two isotopolog ratios: M+1 / M0 (RM+1 for short) and M+2 / M0 (RM+2 for short). Due to the lack of other significant isotopolog peaks in the Ml cluster, the 12Ci peak can be directly converted to a 13C / 12C (R13C) isotope ratio with reasonable accuracy (e.g. by dividing some measure of the peak sizes such as peak height or peak area, which may be measured relative to the background (noise) signal). However, the isotopolog ratio of interest R18O cannot simply be calculated from the RM+2 ratio due to the two significant isotopolog peaks that combine to form the unresolved double peak of the M+2 cluster. Nonetheless, the isotopolog ratio of interest may be extracted from the RM+2 ratio by using simulated mass spectra like those described above to pre-calibrate correction parameters for a specific measurement like the 18O / 16O ratio. These correction parameters are then applied to the data from a real dataset. FIG. 2 shows an embodiment of such a method. Generally, the method 10 comprises a first stage 100 of pre-calibration using theoretical and simulated data to obtain a correction, followed by a second stage 200 of obtaining real data and correcting those data using the correction obtained in the first stage. FIG. 3 shows the method 10 in greater detail. As can be seen, the first stage 100 comprises a step 110 of simulating isotope ratio data, followed by a step 160 of fitting a calibration function to the ratio data to obtain the correction. Then, the second stage 200 comprises a step 210 of obtaining real data, and a step 270 of applying the correction to the ratio of interest obtained from the real data. FIG. 4 breaks down each of the method steps still further. At step 112, a list of isotopologs of the compound of interest (vanillin in this case) is generated. Vanillin is analyzed in positive electrospray ionization as [M+H]+ ion. Therefore, the chemical formula of the analyzed ion of interest is CgHgOg. In this example, the isotopolog / isotope ratio of interest is 18Oi / MO ~ 18O / 16O. To simulate a mass spectrum of the ion of interest, the mass-to-charge ratio (m / z) and the relative abundances of all isotopes present in the compound of interest must be calculated (C, H and O in this example). Specifically, the [M+H]+ ion of vanillin has eight carbon atoms with two possible isotopes (12C and 13C), nine hydrogen atoms with two possible isotopes (1H and 2H) and three oxygen atoms with three possible isotopes (160,17O and 18O). All in all, this leads to the existence 900 isotopolog molecules with different combinations of these isotopes. For each of these 900 isotopologs, the m / z (m / ziSOtopoiog) is calculated by summing the masses of all of the individual isotopes and dividing by the charge of the ion (z which, in this example, is 1), as per: x-M(1JC)+(8-x)-M(1!C),M(+)t(9-y).M(1H)tz-M(“O)+w-M(“O)t(3-z-w)-M(“O) m I ^Isotopolog = ------------------------------- =--------------------------------------------------------------------- (OJ The expected (natural) relative abundance or probability of each isotopolog (piSOtoPoiog) can be calculated by using the natural abundances (p) of the individual isotopes in accordance with eq. 2 given above. This list of masses and relative abundances of all isotopologs can now be used to create an artificial transient. First, the m / z of each isotopolog is used to calculate the frequency (co) it would have in a real mass spectrometer in accordance with eq. 4 above. Then, at step 114, the artificial transient (tran(t)) is created according to the summation of eq. 5 above. At step 116, the artificial transient is now treated like a real transient would be treated by the mass spectrometer. For example, any or all of the following steps may be performed to convert the transient into a mass spectrum: • Apodization • Zeropadding • Enhanced Fourier Transform (eFT) o (transient -> frequency spectrum) • Mass calibration o (frequency spectrum -> m / z spectrum) • Peak picking and Centroiding o (m / z spectrum -> m / z and intensities of isotopolog peaks) The result of step 116 is a list of simulated m / z and relative abundances of all isotopolog peaks that were found in the simulated mass spectrum. At step 118, the m / z and intensities of isotopolog peaks are used to calculate the equivalent simulated isotopolog ratios. As noted above, other measures of peak sizes may be used, such as peak areas. In this example of vanillin analysis, this means: r>13,~ ~ M + ^ simulated j “ ^simulated ~ .,n anu Musimulated RM + 2 simulates M + 2 simulateds MO simulated Now that the ratios have been determined for the natural isotopic abundances, the exercise is repeated for isotopic abundances around the natural values. That is, steps 112 to 118 are repeated multiple times to calibrate a range of different relative abundances / intensities of heavy isotope that is substituted in the related isotopolog peak, as indicated at steps 112' to 118'. In this example of vanillin, the linked isotopologs are the resolvable 13Ci isotopolog peak and the unresolvable 13C2 isotopolog peak. The abundances of both of these linked isotopolog peaks are dependent on the probability of the 13C isotope p(13C). In the first simulated mass spectrum, this probability was assumed to be equal to the natural abundance or the abundance of the 13C isotope in the international reference material (e.g. "Vienna Pee Dee Belemnite" (VPDB)). So, in steps 112' to 118', to account for a range of different abundances of the 13C isotope, the simulations are repeated with different input values for p(13C). In this example, ten additional simulations were carried out with p(13C) varying in between -2OO%o up to +2OO%o around the value derived from the natural abundance of 13C. The input values and the result of all 11 simulations are shown in the following table. Simulation no. p(13C) R^Csimulated RM+2simulated R^Otheoretical 1 0 0.08973 0.00939 0.00587 2 -200 0.07178 0.00816 0.00587 3 -100 0.07627 0.00844 0.00587 4 -50 0.08076 0.00874 0.00587 5 -20 0.08524 0.00906 0.00587 6 -10 0.08883 0.00932 0.00587 7 10 0.09063 0.00946 0.00587 8 20 0.09421 0.00975 0.00587 9 50 0.0987 0.01012 0.00587 10 100 0.10319 0.01051 0.00587 11 200 0.10767 0.01091 0.00587 In the table, p(13C) shows the probability value of the 13C isotope used to simulate the mass spectrum, R13CSimuiated is the ratio of the 13C peak to the MO peak measured from the simulated mass spectrum, RM+2Simuiated is the ratio of the M+2 peak to the MO peak measured from the simulated mass spectrum, and R18Otheoreticai is the theoretical ratio of the 18O peak to the MO peak derived from the input data (i.e. calculated from the ratio of respective probabilities pisotopoiog). Next, the method 10 moves to step 160 where the calibration function is found. At step 162, the results taken from the simulated mass spectra are plotted with a double logarithmic scale. FIG. 5 shows an example of such a plot. The ratio of the resolvable linked isotopolog is plotted on the x-axis as measured from the simulated mass spectrum (R13CSimuiated in the example of vanillin). The difference between the isotopolog ratio of interest as measured from the simulated mass spectrum (here RM+2Simuiated) and the theoretical ratio of interest (here R18Otheoreticai) is plotted on the y-axis. As noted above, R18Otheoreticai can be calculated from p(18O) / p(16O) with the probability of the two isotopes that were used as the input in steps 114 and 114'. Without peak interference, the ratio RM+2 would match the theoretical ratio R18Otheoreticai. Hence, the difference between these RM+2Simuiated and R18Otheoreticai is exactly the inaccuracy that is created from the 18O isotopolog peak interfering with the 13C2-isotopolog peak. Also, the graph of FIG. 5 shows how this difference varies with the ratio of the resolvable linked isotopolog. This difference is what will be corrected for the ratio obtained from the real dataset later, with the correct determination being applied according to the measurable ratio of the resolvable linked isotopolog. At step 164, a linear fit is applied to the double-logarithmic plot and the gradient and intercept of the fit are determined. The gradient and intercept can be used at step 166 to calculate a correction parameter for 18O (CPiso) according to: (7) Qplg0 _ iglog(R13C)*.S(ope- / ntercept _ iglog(R13C)*l.95+0.41 At step 212, real samples are analyzed and datasets are acquired using the mass spectrometer, operating with similar settings as the ones that were used for the simulations of steps 112-118 and 112'-118'. In this example, 21 samples of vanillin with different 613CVpdb, 618OVsmow and 62HVsmow values were analyzed with an Orbitrap mass spectrometer at 7.5k resolution. In addition, to demonstrate the validity of the claimed method, the same 21 samples were analyzed at 180k resolution, in which case the "unresolvable" peaks in the M+2 cluster are resolved (i.e. the M+2 peaks are unresolvable at 7.5k but are resolvable at 180k). Each sample was analyzed by five replicates and in between every single sample injection a reference was injected. The reference was used for drift correction and to reference all samples against the international reference materials VPDB and VSMOW. At the high resolution of 180k, the isotopolog of interest peak (18Oi) and the "unresolvable" linked isotopolog peak (13Cz) are fully resolved. From this measurement, 618OVsMow,i80k can be accurately determined. In the dataset acquired with 7.5k resolution, the 18Oi and 13Cj peaks in the M+2 cluster are not resolved. This measurement results in a RM+lmeasured,7.5k = R13Cmeasured,7.5k and a RM+2measured,7.5k, as determined at step 214. Then, at step 270, the calibration equation (eq. 7) was applied to the 7.5k resolution dataset to calculate 618OVsMow,7.5k. The calibration parameter CPiso was calculated for each sample or reference replicate that was measured using the following equation: pl8zn _ DM | 7 _ cp +1 '-'measured,7.5k ~ ^measured,7.5k ur18O = RM + 2measured75k - 10^R13Cmeasured,r5k^+0.41 The 618Ovsmow,7.5k was calculated based on the R18O values of the sample and the bracketing reference injections using the following equation: / pl8zn \ rl8n _ / '-'measured,sample . \ . nnn , . 6 UVSMOW,7.5k ~ I pl8n 1 I ’ 1UUU '-'measured, referemce / The results of this calculation for one of the analyzed samples in shown in the following table. Injection o CO '□C RM+2 CP 180 r18o 618O Reference Replicate 1 0.09037 0.00975 0.00358 0.00617 - Sample 1 Replicate 1 0.09104 0.00979 0.00363 0.00616 -0.6 Reference Replicate 2 0.09044 0.00974 0.00359 0.00615 - Sample 1 Replicate 2 0.09113 0.00979 0.00364 0.00615 -2.2 Reference Replicate 3 0.09048 0.00976 0.00359 0.00617 - Sample 1 Replicate 3 0.09107 0.00978 0.00364 0.00615 -2.2 Reference Replicate 4 0.09046 0.00975 0.00359 0.00616 - Sample 1 Replicate 4 0.09107 0.00980 0.00364 0.00616 0.5 Reference Replicate 5 0.09050 0.00975 0.00359 0.00616 - Sample 1 Replicate 5 0.09107 0.00978 0.00364 0.00615 -1.5 Reference Replicate 6 0.09045 0.00974 0.00359 0.00615 - The data from the 7.5k measurement corrected in this way is plotted against the data from the 180k measurement for all 21 samples in FIG. 6. This plot shows that the proposed correction of the low-resolution dataset can be used to measured 618O values accurately at low resolution overall resulting in a reduction of the analysis time from 15 min to <1 min. The above example may be applied to any molecule where the target ion has an isotopolog / isotope ratio of interest that is interfering with at least one other isotopolog peak of that same molecule. The intensity of the at least one other isotopolog peak(s) should be related to the intensity of another isotopolog peak in a different isotope cluster of the molecular mass spectrum that is resolvable such that a pair of linked isotopologs exist in which one is unresolvable but the other is resolvable. In case of vanillin, the relation that was used to correct the interference was the relationship between the intensities of the 13Ci and 13Cj isotopologs. The intensities of these peaks are dependent on the probability of 13C-isotope substitution in the molecule and can be calculated using the Bernoulli equation. This same concept can be applied to any other organic molecule that has only two major abundance isotopes (13C and 18O for vanillin). The method could be applied to the analysis of any organic (carboxylic) acids like short-chain fatty acids (SCFA) and long chain fatty acids (LCFA). Additionally, the method could be used for other compounds that mainly consist of carbon and oxygen like carbohydrates (sugars), per- and polyfluoroalkyl substances (PFAS) and any types or organic ketones, aldehydes, esters and ethers. The relation between the 13Ci and 13Cj linked isotopologs is not the only relation that can be used for these corrections. Any other form of multiple isotope substitutions (isotope clumping) like 18Oi and 18O2, 15Ni and 15N2,... can be used just as well. In addition to these multiple isotope substitutions, elements with more than two different isotopes can also be used. One example for this is oxygen (160,17O and 18O), where three different isotopes have different natural abundances and the relation between them is fairly consistent in terrestrial materials. This relationship can be used e.g. to analyze 18O / 16O so as to estimate 17O / 16O to correct the interference between 17Oi and 13Ci isotopologs. The same method can also be used with isotopes of elements like sulfur (32S, 33S, 34S and 36S) and silicon (28Si, 29Si, 30Si). As a second example, the accuracy achievable when measuring 613C maybe increased by up to lO%o using 17O and / or 33S correction in organic molecules. The mass differences of 13C-12C and 17O-16O or 33S-32S are very small at only 0.00086 or 0.004 amu. Therefore, resolving the 13C- and 17O- or 33S-substituted isotopologs of the same molecules requires very high mass resolution and often cannot be resolved at all. Depending on the chemical composition of the compound, this can lead to a measurable impact on the accuracy of a 613C measurement. FIG. 7 shows the error on 513C inflicted by different abundances of 17O in acetate (C2H3O2) and 33S in methionine (C5H11NO2S) as example compounds. For acetate, the plotted difference in 17O leads to errors on 613C of up to O.4%o and in case of methionine the interference with 33S leads to errors of up to 8%o. Depending on the chemical structure of a compound, these effects can be bigger or smaller than the examples displayed in FIG. 7. Resolving other oxygen or sulfur isotopologs requires far better mass resolution. For acetate and methionine, 18O and 34S carrying isotopologs can be resolved and quantified easily. Using the natural relations between 18O and 17O and 34S and 33S, assuming no mass independent fractionation, the 34S / 32S and 18O / 16O ratios can be measured and used to correct the impact of the lighter isotopes on 613C. This concept can be extended to other kinds of element or molecules including elements with more than 2 different stable isotopes like Si, Mg, Cu, Zn, Ti, Hg, etc. As a third example, the present method 10 may be adapted to work for the deconvolution of fully unresolved isotopolog peak clusters. While the examples described above make use of linked isotopologs with one of the isotopologs having a resolvable a peak, this third example uses a method 20 that corrects all isotopolog peaks simultaneously instead of correcting them one at a time using a resolvable linked isotopolog peak. This will again be explained for the example of vanillin, but can be used for any molecule. If all peaks of vanillin are unresolved (e.g. at 7.5k resolution), the creation of artificial transients and mass spectra can be used to determine how each individual isotopolog contributes to each of the 3 peak clusters shown in FIG. 8 (the M+l, M+2 and M+3 peak clusters are shown alongside the M0 peak). FIG. 8 shows portions of a mass spectrum of vanillin, with each peak corresponding to an individual isotopolog peak cluster. Each peak cluster corresponds to the superposition of the contributions from each participating isotopolog. The method 20 is described with reference to FIG. 9. The initial steps 112-118' are as already described with respect to FIG. 4. In summary, at step 112, a list of isotopologs of the compound of interest (vanillin in this case) is generated. The mass-to-charge ratio (m / z) and the relative abundances of all ions present in the compound of interest are calculated (C, H and O in this example). The expected relative abundance or probability of each isotopolog (piSOtoPoiog) is calculated by using the natural abundances (p) of the individual isotopes in accordance with eq. 2 given above. This list of masses and relative abundances of all isotopologs is used to create the artificial transient. First, the m / z of each isotopolog is used to calculate the frequency (co) it would have in a real mass spectrometer in accordance with eq. 4 above. Then, at step 114, the artificial transient (tran(t)) is created according to the summation of eq. 5 above. At step 116, the artificial transient is treated like a real transient would be treated by a mass spectrometer. The result of step 116 is a list of simulated m / z and relative abundances of all isotopolog peaks that were found in the simulated mass spectrum. At step 118, the m / z and intensities of isotopolog peaks are used to calculate the equivalent simulated isotopolog ratios. This exercise is repeated for isotopic abundances around the expected values. That is, steps 112 to 118 are repeated multiple times to calibrate a range of different relative abundances / intensities of heavy isotope that is substituted in the related isotopolog peak, as indicated at steps 112' to 118'. The following steps of the method 20 now differ from that of the method 10 shown in FIG. 4. The use of the artificial transients generated at steps 114 and 114' and subsequent data handling at steps 116 and 116' allows the prediction of the peak interferences. Hence, at step 262, the exact factor (the intensity participation factor) by which the change in each theoretical isotopolog ratio impacts the ratio of the unresolved peak cluster in the simulated mass spectra is calculated. Just as described above, the initial simulation was carried out in steps 112-118 assuming natural abundances for all isotopes. To calculate the participation factors for every single isotopolog in each peak cluster, eleven additional simulations were carried out at steps 112'-118' with 5% increased relative abundance of each of the eleven isotopologs in turn. For example, to calculate the participation factor of the 2Hi isotopolog to the M+l isotope cluster peak at a resolution of 7.5k, the first simulation was carried out assuming the natural abundance of the 2Hi isotope. Consequently, the probability of the 2Hi isotope used as an input for the simulation (p(2H)) was 0.000115. Using eq. 2 above this results in a probability of the p(2Hi) isotopolog of 0.001271 and a theoretical ratio R2Htheoreticai of 0.001401. Carrying out this simulation results in a RM+lSimuiated of 0.93028. In a second simulation, the input value for p(2Hi) was manually increased by 5% to 0.001334. This change also increases the R2Htheoreticai by 0.00007 (5%) to 0.001471. However, the RM+lSimuiated of this second simulation is only increased by 0.000061 compared to the first simulation. The relative participation of the 2Hi isotopolog to the peak cluster M+l can now be calculated as 0 000061 ~ o.87 or 87%. This r ° r 0.00007 same procedure was carried out for 11 isotopologs and the results for 15k and 30k Orbitrap (TM) mass spectrometer resolution is shown in the following table. Peak Cluster Ratio Isotopolog Ratio Intensity Participation Factor at 7.5k Intensity Participation Factor at 30k M+1 / M0 ^ / MO 1.01 1.02 M+1 / M0 ^ / MO 1.00 0.88 M+1 / M0 H / mo 0.87 -0.21 M+2 / M0 ^ / MO 1.00 0.85 M+2 / M0 “cyMo 0.95 0.50 M+2 / M0 “Ci^Oi / MO 0.88 0.00 M+2 / M0 “cyH / MO 0.61 -0.55 M+3 / M0 “Ci^Oi / MO 1.00 0.98 M+3 / M0 M0 0.87 0.20 M+3 / M0 ^O^CVMO 0.79 0.90 M+3 / M0 2h118o1 / mo 0.73 -0.08 Then, at step 264, eqs.l and 2 are used to determine the relationship between each of the isotope ratios of 13C / 12C (x), 2H / 1H (y) and 18O / 16O (z), and then each of the eleven isotopolog ratios are determined. Using this together with the intensity participation factors determined in the table 10 above allows each of the peak cluster ratios to be described by equations that are only dependent on the three isotope ratios x, y and z. The resulting system of equations are shown here for 7.5k resolution: 0=8* 1.01 * x + 9 * 0.87 * y + 1.00 * 0.57 * z — R M + 1\ . M0 / (7) 0 = 3* 1.00 * z + 0.189457410732097 1 + z * 0.189457410732097 + z * 0.88 G + x) * G + z * 0.189457410732097 + z) * 8 * 3 V 1 nn , / G + x) * 56 -------jj--------------------- I * 1.00 + I ----------3— (iTx) * (1 + z * 0.189457410732097 + z) / \ G"Tx) * 0.87 / 0.189457410732097 \ / z \ , kZ * 1 + z * 0.189457410732097 + z? * kl + z * 0.189457410732097 + z? * 3 * ___________1___________f 1 + z * 0.189457410732097 + z7 (l"+y) * G + z * 0.189457410732097 + z) * 9 * 3 n,n / M + 3\ * °-79 +-----1--------------------* 0.73 - R (_J_W_________-_________1 M0 ’ U + y7 kl + z * 0.189457410732097 + z / Then, at step 212, real data is obtained from the mass spectrometer. The three ratios of R ), R () and R () are values are measured from the real scans at step 214. The k MO / k MO / k MO / measured ratios are put into the equations 7, 8 and 9 at step 272 (from every scan or the averaged 5 ratios of every sample or sample block or injection). Putting each of the three values into equations 7, 8 and 9 results in three equations with three unknowns. At step 274, a simple solve function (e.g. scipy.optimize.fsolve, python) can be used to solve these equations and give all three isotope ratios 13C / 12C (x), (y) and 18O / 16O (z). The same concept can be applied to any other compound / measurement as long as the 10 number of isotope cluster peak that were measured is equal or greater than the number of different elements in the compounds chemical structure. It will be understood by those skilled in the art that the invention is not limited to the embodiments shown and that many additions and modification may be made without departing from the scope of the invention as defined in the appending claims.

Claims

1. A method of analysing isotopes of an element present in a compound of interest from a mass spectrum obtained by a Fourier transform mass spectrometer, the method comprising:generating simulated transients that would be measured in the mass spectrometer when measuring a sample of the compound of interest at one or more selected resolutions of the mass spectrometer, the simulated transients corresponding to samples of the compound of interest with different relative isotopic abundances;processing the simulated transients to produce respective simulated mass spectra data;comparing the simulated mass spectra data to theoretical mass spectra data to determine a correction to be applied to real mass spectra data to account for changes in isotopolog peak sizes caused by interference between unresolved isotopolog peaks.

2. The method of claim 1, further comprising;measuring one or more corresponding real transients from a sample of the compound of interest using the mass spectrometer at the selected resolution;processing the one or more real transients in the same way as the simulated transients to produce real mass spectrum data;calculating a peak ratio from the real mass spectrum data;applying the correction to the peak ratio calculated from the real mass spectrum data to obtain a corrected ratio; andusing the corrected ratio to determine information about the isotopic composition of the compound of interest.

3. The method of claim 1 or 2, wherein generating the simulated transients comprises summing the contributions from a plurality of isotopologs present in the compound of interest, with the amplitude of each contribution being weighted according to the relative isotopic abundances of the isotopes present in that isotopolog.

4. The method of claim 3, wherein generating the simulated transients comprises including contributions from the plurality of isotopologs present in the compound of interest according to the natural isotopic abundances of the isotopes present in compound of interest.

5. The method of claim 4, wherein generating the simulated transients comprises generating simulated transients by varying the relative isotopic abundances of the isotopes present in compound of interest thereby producing different relative abundances of the isotopologs.

6. The method of any of claims 3 to 5, wherein summing the contributions from the plurality of isotopologs present in the compound of interest comprises determining the frequency of the contribution according to the mass to charge ratio of the associated isotopolog.

7. The method of any of any preceding claim, further comprising:determining first and second isotopes of an element of interest present in a compound to be analysed, wherein the first isotope is the lightest isotope and the second isotope is a heavier isotope;identifying first and second isotopologs of interest that include the first isotope and second isotope respectively, the first isotopolog being the lightest isotopolog that generates a single, isolated peak when mass spectrum data are obtained by the mass spectrometer at the selected resolution,identifying an isotopolog peak cluster containing a peak generated by the second isotopolog of interest when mass spectrum data are obtained by the mass spectrometer at the selected resolution, wherein the selected resolution is not sufficient to resolve the peak generated by the second isotopolog of interest from an interfering peak in the isotopolog peak cluster that interferes with the peak generated by the second isotopolog of interest;identifying the interfering isotopolog that contributes the interfering peak to the isotopolog peak cluster;identifying a linked isotopolog of the interfering isotopolog containing the same isotope as the interfering isotopolog, wherein that isotope is a heavier isotope of a further element present in the compound of interest, and the interfering isotopolog and linked isotopolog form a pair of an unresolvable linked isotopolog and a resolvable linked isotopolog.

8. The method of claim 7, further comprising:determining mass to charge ratios of each isotopolog of the group of isotopologs, the group of isotopologs comprising the first isotopolog of interest, the second isotopolog of interest, and the linked isotopologs, based on the atomic masses of the isotopes present in each isotopolog;determining the frequency of the contribution that each isotopolog of the group of isotopologs will contribute to the transient signal;calculating proportions of each isotopolog from (i) the natural abundances of the isotopes present in each isotopolog and (ii) generated abundances that vary around the natural abundances of the isotopes present in each isotopolog;determining theoretical ratios of first and second isotopes from the calculated proportions;generating simulated transients by summing the contribution from each isotopolog of the group of isotopologs based on the calculated proportions of each isotopolog;processing the simulated transients to produce simulated mass spectra data;determining simulated ratios of first and second isotopes from the simulated mass spectra data;determining the ratio of the heavier isotope of the further element to the lightest isotope of the further element from the simulated mass spectra data by dividing the size of the peak produced by the resolvable linked isotopolog by the corresponding size of the peak produced by the lightest isotopolog; anddetermining the correction by determining a relationship between (i) the difference in (a) the ratio of the size of the isotopolog cluster peak to the corresponding size of the peak of the lightest isotopolog in the simulated mass spectra data and (b) the theoretical ratios of first and second isotopes of interest, and (ii) the determined ratio of the heavier isotope to the lightest isotope of the further element.

9. The method of claim 8 when dependent upon claim 2, further comprising:measuring the ratio of the first and second isotopes of interest using the real mass spectrum data; andmodifying the measured ratio using the relationship.

10. The method of any of claims 7 to 9, wherein the resolvable linked isotopolog is an isotopolog with a single substitution of the isotope of the further element and the unresolvable linked isotopolog is an isotopolog with multiple substitutions of the isotope of the further element.

11. The method of claim 10, wherein the unresolvable linked isotopolog contains two 13C isotopes and the second isotopolog of interest is an isotopolog with a single 18O substitution.

12. The method of any of claims 7 to 11, wherein the compound to be analysed comprises an organic molecule that contains carbon and oxygen, such as vanillin, PFAS, an organic alcohol, acid, aldehyde or ether.

13. The method of any of any preceding claim, comprising:determining isotopes of elements of interest present in a compound to be analysed;identifying isotopologs present in the compound;determining mass to charge ratios of the isotopologs based on the atomic masses of the isotopes present in each isotopolog;determining the frequency of the contribution that each isotopolog of the group of isotopologs will contribute to the transient signal;calculating proportions of each isotopolog from (i) the natural abundances of the isotopes present in each isotopolog and (ii) from generated abundances that vary around the natural abundances of the isotopes present in each isotopolog.

14. The method of claim 13, further comprising:for each isotope, determining the theoretical difference in isotopolog peak sizes from the calculated proportions for isotopologs containing varying abundances of that isotope;generating simulated transients by summing the contribution from each isotopolog based on the calculated proportions of each isotopolog;processing the simulated transients to produce respective simulated mass spectra data;for each isotope, determining the simulated difference in isotopolog peak sizes from the simulated mass spectra data for the isotopologs used to calculate the theoretical difference in isotopolog peak sizes;for each isotope, determining an intensity participation factor by comparing the simulated difference in isotopolog peak sizes to the theoretical difference for that isotope;determining isotope ratios of each isotope based on the calculated proportions;for each isotopolog peak cluster, forming an equation linking the size of the peak to the isotope ratios and the intensity participation factors of the isotopes present in the isotopologs in that isotopolog peak cluster.

15. The method of claim 14 when dependent upon claim 2, further comprising:measuring the ratio of the peak sizes of each isotopolog peak cluster to the peak size of the lightest isotopolog peak using the real mass spectrum data; andsubstituting the measured ratio into the equation for each isotopolog peak cluster; and solving the equations to determine corrected isotope ratios for the real mass spectrum data.

16. The method of any of claims 13 to 15, wherein at least two isotopologs have peaks in a peak cluster that interfere with each other, and the at least two isotopologs are isotopologs of an element with three or more different isotopes.5 17. The method of claim 16, wherein the three or more different isotopes are oxygenisotopes and the interfering peaks arise from a 17O-substituted isotopolog and a 18O isotopolog.

18. A computer program comprising computer program instructions that, when executed by one or more computer processors, cause the one or more computer processors to perform the 10 method of any preceding claim.

19. A computer readable medium having stored thereon the computer program according to claim 18.15 20. A mass spectrometer comprising one or more computer processors and computermemory having stored therein a computer program according to claim 18.s

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