Quantitative determination of isotope ratios from experimental isotopic distributions

Isotope variability due to natural processes provides important information for studying a variety of complex natural phenomena from the origins of a particular sample to the traces of biochemical reaction mechanisms. These measurements require high-precision determination of isotope ratios of a particular element involved. Isotope ratio mass spectrometers (IRMS) are widely employed tools for such a high-precision analysis, which have some limitations. This work aims at overcoming the limitations inherent to IRMS by estimating the elemental isotopic abundance from the experimental isotopic distribution. In particular, a computational method has been derived that allows the calculation of 13C/12C ratios from the whole isotopic distributions, given certain caveats, and these calculations are applied to several cases to demonstrate their utility. The limitations of the method in terms of the required number of ions and S/N ratio are discussed. For high-precision estimates of the isotope ratios, this method requires very precise measurement of the experimental isotopic distribution abundances, free from any artifacts introduced by noise, sample heterogeneity, or other experimental sources.     

Isotopic peak intensity ratio based algorithm for determination of isotopic clusters and monoisotopic masses of polypeptides from high-resolution mass spectrometric data

Determining isotopic clusters and their monoisotopic masses is a first step in interpreting complex mass spectra generated by high-resolution mass spectrometers. We propose a mathematical model for isotopic distributions of polypeptides and an effective interpretation algorithm. Our model uses two types of ratios: intensity ratio of two adjacent peaks and intensity ratio product of three adjacent peaks in an isotopic distribution. These ratios can be approximated as simple functions of a polypeptide mass, the values of which fall within certain ranges, depending on the polypeptide mass. Given a spectrum as a peak list, our algorithm first finds all isotopic clusters consisting of two or more peaks. Then, it scores clusters using the ranges of ratio functions and computes the monoisotopic masses of the identified clusters. Our method was applied to high-resolution mass spectra obtained from a Fourier transform ion cyclotron resonance (FTICR) mass spectrometer coupled to reverse-phase liquid chromatography (RPLC). For polypeptides whose amino acid sequences were identified by tandem mass spectrometry (MS/MS), we applied both THRASH-based software implementations and our method. Our method was observed to find more masses of known peptides when the numbers of the total clusters identified by both methods were fixed. Experimental results show that our method performed better for isotopic mass clusters of weak intensity where the isotopic distributions deviate significantly from their theoretical distributions. Also, it correctly identified some isotopic clusters that were not found by THRASH-based implementations, especially those for which THRASH gave 1 Da mismatches. Another advantage of our method is that it is very fast, much faster than THRASH that calculates the least-squares fit.     

Stable isotope assisted assignment of elemental compositions for metabolomics

Assignment of individual compound identities within mixtures of thousands of metabolites in biological extracts is a major challenge for metabolomic technology. Mass spectrometry offers high sensitivity over a large dynamic range of abundances and molecular weights but is limited in its capacity to discriminate isobaric compounds. In this article, we have extended earlier studies using isotopic labeling for elemental composition elucidation (Rodgers, R. P.; Blumer, E. N.; Hendrickson, C. L.; Marshall, A. G. J. Am. Soc. Mass Spectrom. 2000, 11, 835-40) to limit the formulas consistent with any exact mass measurement by comparing observations of metabolites extracted from Arabidopsis thaliana plants grown with (I) (12)C and (14)N (natural abundance), (II) (12)C and (15)N, (III) (13)C and (14)N, or (IV) (13)C and (15)N. Unique elemental compositions were determined over a dramatically enhanced mass range by analyzing exact mass measurement data from the four extracts using two methods. In the first, metabolite masses were matched with a library of 11,000 compounds known to be present in living cells by using values calculated for each of the four isotopic conditions. In the second method, metabolite masses were searched against masses calculated for a constrained subset of possible atomic combinations in all four isotopic regimes. In both methods, the lists of elemental compositions from each labeling regime were compared to find common formulas with similar retention properties by HPLC in at least three of the four regimes. These results demonstrate that metabolic labeling can be used to provide additional constraints for higher confidence formula assignments over an extended mass range.     

Interpreting the charge state assignment in electrospray mass spectra of bioparticles

In electrospray ionization mass spectra of heterogeneous protein complexes and other bioparticles, accurate mass determination is often hampered by the inaccuracy in determination of the charge states for individual signals. Here, we describe an algorithm that automatically minimizes the standard deviation in a series of related ion peaks with varying numbers of charges. The algorithm assumes that the mass is invariant and allows the determination of the correct charge state in a peak series. The analysis results in a periodic pattern, which can be interpreted as a harmonic oscillator, when the minimum standard deviation of a charge state series is found. We observed that a mass resolution of much less than 1000 in the acquired mass spectra is sufficient to achieve a correct charge state assignment. Moreover, the boundaries of mixed species can be identified by examining the loss of periodicity in the pattern of the analysis. We tested our algorithm successfully on novel spectra and on spectra reported in the literature with sample masses up to several million Dalton, e.g., viral particles, polyethylene glycol polymers, and polystyrene nanoparticles.     

Determination of elemental compositions from mass peak profiles of the molecular ion (m) and the m + 1 and m + 2 ions

The relative abundances of M + 1 and M + 2 ions help to identify the elemental composition of the molecular ion (M). But scan speed, sensitivity, and resolution limitations of mass spectrometers have impeded determination of these abundances. Mass peak profiling from selected ion recording data (MPPSIRD) provided faster sampling and enhanced sensitivity, which permitted use of higher resolution. M + 2 profiles having only a few percent of the ion abundance of M were monitored at 20?000 resolution. The relative abundances, exact masses, and shapes of M, M + 1, and M + 2 mass peak profiles were determined. By applying five criteria based on these quantities, elemental compositions were determined even for ions too large (up to 766 Da) to be uniquely assigned from their exact mass and accuracy limits alone. A profile generation model (PGM) was written to predict these resolution-dependent quantities by considering all M + 1 and M + 2 ions for each candidate composition. The model also provided assurance that no other compositions were possible. Characterization of the M + 1 and M + 2 profiles by MPPSIRD and the PGM greatly expanded the practical ability of high-resolution mass spectrometry to determine elemental compositions.     

Isotopic analyses based on the mass spectrum of carbon dioxide

Measurements of carbon and oxygen isotopic abundances are commonly based on the mass spectrum of carbon dioxide, but analysis of that spectrum is not trivial because three isotope ratios (17O/16O, 18O/16O, and 13C/12C) must be determined from only two readily observable ion-current ratios (45/44 and 46/44). Here, approaches to the problem are reassessed in the light of new information regarding the distribution of oxygen isotopes in natural samples. It is shown that methods of calculation conventionally employed can lead to systematic errors in the computed abundance of 13C and that these errors may be related to incorrect assessment of the absolute abundance of 17O. Further, problems arising during the analysis of samples enriched by admixture of 18O-labeled materials are discussed, and it is shown (i) that serious inaccuracies arise in the computed abundance of 17O and 13C if methods of calculation conventionally employed in the analysis of natural materials are applied to material labeled with 18O but (ii) that computed fractional abundances of 18O are always within 0.4% of the correct result. Methods for exact calculation of two isotope ratios when the third is known are presented and discussed, and a more exact approach to the computation of all three isotope ratios in natural materials is given.     

Compartment modeling for mammalian protein turnover studies by stable isotope metabolic labeling

Protein turnover studies on a proteome scale based on metabolic isotopic labeling can provide a systematic understanding of mechanisms for regulation of protein abundances and their transient behaviors. At this time, these large-scale studies typically utilize a simple kinetic model to extract protein dynamic information. Although many high-quality, protein isotope incorporation data are available from those experiments, accurate and additionally useful protein dynamic information cannot be extracted from the experimental data by use of the simple kinetic models. In this paper, we describe a formal connection between data obtained from elemental isotope labeling experiments and the well-known compartment modeling, and we demonstrate that an appropriate application of a compartment model to turnover of proteins from mammalian tissues can indeed lead to a better fitting of the experimental data.     

Automatic deconvolution of isotope-resolved mass spectra using variable selection and quantized peptide mass distribution

We present an algorithm for the deconvolution of isotope-resolved mass spectra of complex peptide mixtures where peaks and isotope series often overlap. The algorithm formulates the problem of mass spectrum deconvolution as a classical statistical problem of variable selection, which aims to interpret the spectrum with the least number of peptides. The LASSO method is used to perform automatic variable selection. The algorithm also makes use of the quantized distribution of peptide masses in the NCBInr database after in silico trypsin digestion as filters to aid the deconvolution process. Errors in the expected isotope pattern are accounted for to avoid spurious isotope series. The effectiveness of the algorithm is demonstrated with annotated ESI spectrum of known peptides for which the peaks and isotope series are highly overlapping. The algorithm successfully finds all correct masses in the experimental spectrum, except for one spectrum where an additional refinement procedure is required to obtain the correct results. Our results compare favorably to those from a widely used commercial program.     

Conversion of carbon into CF4 for SI-traceable measurements of absolute carbon isotope amount ratios: a feasibility study

The feasibility of performing SI-traceable carbon isotope amount ratio measurements following conversion of carbon into CF4 was studied. A procedure for the direct fluorination of carbon with elemental fluorine was developed, and the conversion step was checked for losses, blank contributions, and the absence of systematic isotope effects. Gas chromatography was used to identify and quantify the gaseous fluorination products and to isolate CF4 from byproducts. After fluorination of graphite carbon, CF4 and perfluoroalkanes with up to six carbon atoms were observed as reaction products. Within an uncertainty of 10%, the graphite carbon was fully recovered in the gaseous carbon fluorides, with the main product being CF4 (80-90%) and C2F6 as the major byproduct. The fluorination and GC procedures were found to introduce an alteration not bigger than 0.03 +/- 0.04/1000 on the isotopic composition of CF4. Carbon blank contributions introduced during the fluorination procedure were below 0.5% relative to a typical sample of 4 mg of carbon. For two of the materials investigated, the carbon isotope ratios measured on a differential mass spectrometer were reproducible within a standard deviation of approximately 0.1/1000 for several individual fluorinations. For these materials, the developed fluorination procedure is a straightforward process, which can be used as a foundation to establish SI-traceable measurements of carbon isotope amount ratios. However, for the third graphite material the formation of byproducts (C2F6-C6F14) was found to induce significant isotopic fractionation.     

Reduction of nonpolar amino acids to amino alcohols to enhance volatility for high-precision isotopic analysis

Amino acids are routinely derivatized using carbon-containing groups prior to gas chromatography continuous-flow isotope ratio mass spectrometry (GCC-IRMS). Derivative C contaminates analyte C because the entire derivatized compound is combusted to CO2. Correction procedures are required to extract the analyte isotope ratio. We present a method for reduction of six nonpolar amino acids to their corresponding amino alcohols, demonstrate a GC strategy to produce acceptable peak shapes from the resulting strongly H-bonding analytes, and present isotopic analysis for amino acids and their corresponding amino alcohols to evaluate any possible isotopic fractionation. Alanine, valine, leucine, isoleucine, methionine, or phenylalanine was reduced using NaBH4 in THF with I2 as an electrophile. Reactions were performed with 2 g of analyte to permit isotopic analysis by conventional elemental analysis-IRMS. All reactions were quantitative as assessed by IR spectra, melting points, and GC. Recovery from the reaction mixture was 60-84%. GC separation of a mixture of the six amino alcohols was achieved using a thick stationary-phase (5 microm) capillary column to avoid tailing due to hydrogen bonding to the walls of the fused-silica capillary. The reproducibility of GCC-IRMS determinations of amino alcohols averaged SD(613C) = 0.25 +/- 0.19%. The absolute differences between delta13C of amino acids measured by an elemental analyzer coupled to IRMS and amino alcohols measured by GCC-IRMS was delta613C = 0.14% and showed no general trend. Reactions performed with 2 mg of analyte yielded equivalent chromatograms. These data indicate that the reduction method does not induce isotopic fractionation and can be used for continuous-flow isotopic analysis to avoid addition of contaminating carbon.     

Photocounting statistics associated with temperature fluctuations in semiconductor lasers

Photoelectron counting distributions are obtained for sources which obey compound Poisson statistics. Various cases are considered in which the sources (semiconductor lasers) emit coherent light and their intensity fluctuates in accordance with a Gaussian distribution of operating temperatures. The lasers are otherwise assumed to be ideal, and the quantum efficiency of the detector is assumed to be unity. This paper represents an ideal situation where the source is the only concern in the calculation of the photoelectron counting distributions. It is found that for large temperature fluctuations (a > 10 K), a substantial downward shift of the peak of the photon probability density function is observed. The function becomes more asymmetric and the mean value decreases as the standard deviation of the temperature increases.     

Quantitative LC-MS of polymers: determining accurate molecular weight distributions by combined size exclusion chromatography and electrospray mass spectrometry with maximum entropy data processing

We report on the successful application of size exclusion chromatography (SEC) combined with electrospray ionization mass spectrometry (ESI-MS) and refractive index (RI) detection for the determination of accurate molecular weight distributions of synthetic polymers, corrected for chromatographic band broadening. The presented method makes use of the ability of ESI-MS to accurately depict the peak profiles and retention volumes of individual oligomers eluting from the SEC column, whereas quantitative information on the absolute concentration of oligomers is obtained from the RI-detector only. A sophisticated computational algorithm based on the maximum entropy principle is used to process the data gained by both detectors, yielding an accurate molecular weight distribution, corrected for chromatographic band broadening. Poly(methyl methacrylate) standards with molecular weights up to 10 kDa serve as model compounds. Molecular weight distributions (MWDs) obtained by the maximum entropy procedure are compared to MWDs, which were calculated by a conventional calibration of the SEC-retention time axis with peak retention data obtained from the mass spectrometer. Comparison showed that for the employed chromatographic system, distributions below 7 kDa were only weakly influenced by chromatographic band broadening. However, the maximum entropy algorithm could successfully correct the MWD of a 10 kDa standard for band broadening effects. Molecular weight averages were between 5 and 14% lower than the manufacturer stated data obtained by classical means of calibration. The presented method demonstrates a consistent approach for analyzing data obtained by coupling mass spectrometric detectors and concentration sensitive detectors to polymer liquid chromatography.     

Windowed Fourier transform for fringe pattern analysis: theoretical analyses

A windowed Fourier ridges (WFR) algorithm and a windowed Fourier filtering (WFF) algorithm have been proposed for fringe pattern analysis and have been demonstrated to be versatile and effective. Theoretical analyses of their performances are of interest. Local frequency and phase extraction errors by the WFR and WFF algorithms are analyzed in this paper. Effectiveness of the WFR and WFF algorithms will thus be theoretically proven. Consider four phase-shifted fringe patterns with local quadric phase [c(20)=c(02)=0.005 rad/(pixel)(2)], and assume that the noise in these fringe patterns have mean values of zero and standard deviations the same as the fringe amplitude. If the phase is directly obtained using the four-step phase-shifting algorithm, the phase error has a mean of zero and a standard deviation of 0.7 rad. However, when using the WFR algorithm with a window size of sigma(x)=sigma(y)=10 pixels, the local frequency extraction error has a mean of zero and a standard deviation of less than 0.01 rad/pixel and the phase extraction error in the WFR algorithm has a mean of zero and a standard deviation of about 0.02 rad. When using the WFF algorithm with the same window size, the phase extraction error has a mean of zero and a standard deviation of less than 0.04 rad and the local frequency extraction error also has a mean of zero and a standard deviation of less than 0.01 rad/pixel. Thus, an unbiased estimation with very low standard deviation is achievable for local frequencies and phase distributions through windowed Fourier transforms. Algorithms applied to different fringe patterns, different noise models, and different dimensions are discussed. The theoretical analyses are verified by numerical simulations.     

Evaluation of the Isotope Ratio Performance of an Axial Time-of-Flight ICP Mass Spectrometer

The isotope ratio performance of an axial time-of-flight ICP mass spectrometer (Renaissance TOF-ICPMS, LECO Corp.) was evaluated. The isotope ratio precision, expressed as the relative standard deviation (RSD) for 10 successive measurements, was evaluated using multielement standard solutions with analyte concentrations of 50-500 μg/L. The influence of the acquisition time per replicate measurement was studied by varying it between 0.5 and 300 s. For an acquisition time of 30 s per replicate and an elemental concentration of 500 μg/L, typical isotope ratio precisions of ≤0.05% RSD were obtained. The fact that this isotope ratio precision can be obtained for many ratios simultaneously is an especially attractive feature of TOF-ICPMS. In contrast to what was expected, increasing the acquisition time per replicate to values of >30 s resulted in a slightly deteriorated isotope ratio precision. At short acquisition times (<10 s), isotope ratio precisions similar to, or better than, the best values ever reported for quadrupole-based instruments were obtained. The latter observation remained valid when working with transient signals of corresponding duration. Mass discrimination was observed to be analogous to that observed with other types of ICPMS instrumentation (～1% per mass unit at midmass). The accuracy attainable was evaluated by comparing Pb isotopic results for a "natural" Pb standard solution obtained by TOF-ICPMS with those obtained by thermal ionization mass spectrometry.     

Measurement of the isotope enrichment of stable isotope-labeled proteins using high-resolution mass spectra of peptides

Stable isotope-enriched molecules are used as internal standards and as tracers of in vivo substrate metabolism. The accurate conversion of measured ratios in the mass spectrometer to mole ratios is complicated because a polyatomic molecule containing enriched atoms will result in a combinatorial distribution of isotopomers depending on the enrichment and number of "labeled" atoms. This effect could potentially cause a large error in the mole ratio measurement depending on which isotope peak or peaks were used to determine the ratio. We report a computational method that predicts isotope distributions over a range of enrichments and compares the predicted distributions to experimental peptide isotope distributions obtained by Fourier transform ion cyclotron resonance mass spectrometry. Our approach is accurate with measured enrichments within 1.5% of expected isotope distributions. The method is also precise with 4.9, 2.0, and 0.8% relative standard deviations for peptides containing 59, 79, and 99 atom % excess (15)N, respectively. The approach is automated making isotope enrichment calculations possible for thousands of peptides in a single muLC-FTICR-MS experiment.     

Simultaneous determination of species-specific isotopic composition of Hg by gas chromatography coupled to multicollector ICPMS

This work presents the simultaneous online determination of the isotopic composition of different Hg species in a single sample by the hyphenation of gas chromatography (GC) with multicollector-inductively coupled plasma mass spectrometry (MC-ICPMS). With the use of commercially available instrumentation, precise and accurate species-specific Hg isotope delta values (per mil deviation of the Hg isotope ratio in the sample relative to a reference standard) have been obtained online from consecutive GC transient signals. The use of isothermal temperature programs to extend the elution of the Hg species, the proper selection of the peak integration window, as well as the preconcentration of real samples are critical to provide optimal counting statistics. Also, isotope ratio drift during transient signal elution was overcome by introducing a mixed Hg(II) and MeHg standard bracketing scheme and expressing all results using the delta-notation relative to SRM NIST-3133. Using the proposed methodology, we have obtained an external 2SD precision of 0.56 per thousand for delta (202)Hg that is more than 10 times smaller than the overall Hg stable isotope variation thus far observed in terrestrial samples. The measurement of species-specific Hg isotopic composition relative to SRM NIST-3133 has been validated versus two other analytical techniques, i.e., conventional nebulization (CN) of Hg(II) solution and cold vapor (CV) generation of Hg (0) vapor. A good agreement between the species-specific delta values obtained by the different techniques has been obtained in secondary fractionated reference standard (UM-Almaden) and environmental matrixes, i.e., BCR-CRM 464 (tuna fish) and IAEA-085 (human hair). The results show mass-dependent and mass-independent fractionation in environmental samples, i.e., mass-independent fractionation of odd isotopes (199)Hg and (201)Hg in tuna fish was observed. This methodology provides new possibilities for the future study of species-specific stable isotope geochemistry of Hg and other trace metals.     

Reduction of chemical formulas from the isotopic peak distributions of high-resolution mass spectra

A method has been developed for the reduction of the chemical formulas of compounds in complex mixtures from the isotopic peak distributions of high-resolution mass spectra. The method is based on the principle that the observed isotopic peak distribution of a mixture of compounds is a linear combination of the isotopic peak distributions of the individual compounds in the mixture. All possible chemical formulas that meet specific criteria (e.g., type and number of atoms in structure, limits of unsaturation, etc.) are enumerated, and theoretical isotopic peak distributions are generated for each formula. The relative amount of each formula is obtained from the accurately measured isotopic peak distribution and the calculated isotopic peak distributions of all candidate formulas. The formulas of compounds in simple spectra, where peak components are fully resolved, are rapidly determined by direct comparison of the calculated and experimental isotopic peak distributions. The singular value decomposition linear algebra method is used to determine the contributions of compounds in complex spectra containing unresolved peak components. The principles of the approach and typical application examples are presented. The method is most useful for the characterization of complex spectra containing partially resolved peaks and structures with multiisotopic elements.     

Improved mass defect model for theoretical tryptic peptides

Improvements in the mass accuracy and resolution of mass spectrometers have greatly aided mass spectrometry-based proteomics in profiling complex biological mixtures. With the use of innovative bioinformatics approaches, high mass accuracy and resolution information can be used for filtering chemical noise in mass spectral data. Using our recent algorithmic developments, we have generated the mass distributions of all theoretical tryptic peptides composed of 20 natural amino acids and with masses limited to 3.5 kDa. Peptide masses are distributed discretely, with well-defined peak clusters separated by empty or sparsely populated trough regions. Accurate models for peak centers and widths can be used to filter peptide signals from chemical noise. We modeled mass defects, the difference between monoisotopic and nominal masses, and peak centers and widths in the peptide mass distributions. We found that peak widths encompassing 95% of all peptide sequences are substantially smaller than previously thought. The result has implications for filtering out larger stretches of the mass axis. Mass defects of peptides exhibit an oscillatory behavior which is damped at high mass values. The periodicity of the oscillations is about 14 Da which is the most common difference between the masses of the 20 natural amino acids. To determine the effects of amino acid modifications on our findings, we examined the mass distributions of peptides composed of the 20 natural amino acids, oxidized Met, and phosphorylated Ser, Thr, and Tyr. We found that extension of the amino acid set by modifications increases the 95% peak width. Mass defects decrease, reflecting the fact that the average mass defect of natural amino acids is larger than that of oxidized Met. We propose that a new model for mass defects and peak widths of peptides may improve peptide identifications by filtering chemical noise in mass spectral data.     

Identification of uncommon plant metabolites based on calculation of elemental compositions using gas chromatography and quadrupole mass spectrometry

Unknown compounds in polar fractions of Arabidopsis thaliana crude leaf extracts were identified on the basis of calculations of elemental compositions obtained from gas chromatography/low-resolution quadrupole mass spectrometric data. Plant metabolites were methoximated and silylated prior to analysis. All known peaks were used as internal references to construct polynomial recalibration curves of from raw mass spectrometric data. Mass accuracies of 0.005 +/- 0.003 amu and isotope ratio errors of 0.5 +/- 0.3% (A + 1/A), respectively, 0.3 +/- 0.2% (A + 2/A), could be achieved. Both masses and isotope ratios were combined when the elemental compositions of unknown peaks were calculated. After calculation, compound identities were elucidated by searching metabolic databases, interpreting spectra, and, finally, by comparison with reference compounds. Sum formulas of more than 70 peaks were determined throughout single GC/MS chromatograms. Exact masses were confirmed by high-resolution mass spectrometric data. More than 15 uncommon plant metabolites were identified, some of which are novel in Arabidopsis, such as tartronate semialdehyde, citramalic acid, allothreonine, or glycolic amide.     

Measurement of total acid number (TAN) and TAN boiling point distribution in petroleum products by electrospray ionization mass spectrometry

We report a new method for rapid measurement of total acid number (TAN) and TAN boiling point (BP) distribution for petroleum crude and products. The technology is based on negative ion electrospray ionization mass spectrometry (ESI-MS) for selective ionization of petroleum acid and quantification of acid structures and molecular weight distributions. A chip-based nanoelectrospray system enables microscale (<200 mg) and higher throughput (20 samples/h) measurement. Naphthenic acid structures were assigned based on nominal masses of a set of predefined acid structures. Stearic acid is used as an internal standard to calibrate ESI-MS response factors for quantification purposes. With the use of structure-property correlations, boiling point distributions of TAN values can be calculated from the composition. The rapid measurement of TAN BP distributions by ESI is demonstrated for a series of high-TAN crudes and distillation cuts. TAN values determined by the technique agree well with those by the titration method. The distributed properties compare favorably with those measured by distillation and measurement of TAN of corresponding cuts.