Correcting for the effects of natural abundance in stable isotope resolved metabolomics experiments involving ultra-high resolution mass spectrometry
© Moseley; licensee BioMed Central Ltd. 2010
Received: 29 October 2009
Accepted: 17 March 2010
Published: 17 March 2010
Stable isotope tracing with ultra-high resolution Fourier transform-ion cyclotron resonance-mass spectrometry (FT-ICR-MS) can provide simultaneous determination of hundreds to thousands of metabolite isotopologue species without the need for chromatographic separation. Therefore, this experimental metabolomics methodology may allow the tracing of metabolic pathways starting from stable-isotope-enriched precursors, which can improve our mechanistic understanding of cellular metabolism. However, contributions to the observed intensities arising from the stable isotope's natural abundance must be subtracted (deisotoped) from the raw isotopologue peaks before interpretation. Previously posed deisotoping problems are sidestepped due to the isotopic resolution and identification of individual isotopologue peaks. This peak resolution and identification come from the very high mass resolution and accuracy of FT-ICR-MS and present an analytically solvable deisotoping problem, even in the context of stable-isotope enrichment.
We present both a computationally feasible analytical solution and an algorithm to this newly posed deisotoping problem, which both work with any amount of 13C or 15N stable-isotope enrichment. We demonstrate this algorithm and correct for the effects of 13C natural abundance on a set of raw isotopologue intensities for a specific phosphatidylcholine lipid metabolite derived from a 13C-tracing experiment.
Correction for the effects of 13C natural abundance on a set of raw isotopologue intensities is computationally feasible when the raw isotopologues are isotopically resolved and identified. Such correction makes qualitative interpretation of stable isotope tracing easier and is required before attempting a more rigorous quantitative interpretation of the isotopologue data. The presented implementation is very robust with increasing metabolite size. Error analysis of the algorithm will be straightforward due to low relative error from the implementation itself. Furthermore, the algorithm may serve as an independent quality control measure for a set of observed isotopologue intensities.
Application of mass spectrometry to stable isotope tracing experiments for the elucidation of glucose dates back to at least the early 1980's [1, 2]. The general scheme for these experiments is to supply a labeled precursor such as uniformly-labeled 13C glucose ([U-13C]-glucose) to a bacterial culture, tissue culture, or a whole multicellular organism and then extract a set of cellular or excreted metabolites for analysis [3, 4]. For identified metabolites, specific patterns of isotopologues are usually observed, which are then interpreted within the context of known cellular metabolic pathways [3–5]. Recently, we applied this technique to elucidate specific aspects of lipid metabolism .
The ultra-high resolution capability of Fourier transform-ion cyclotron resonance-mass spectrometry (FT-ICR-MS) makes it possibility to identify simultaneously hundreds, if not thousands, of metabolites from crude cell extracts without the need for chromatographic separation . The better than 1 ppm mass accuracy of state-of-the-art FT-ICR-MS is often high enough to provide mass-to-charge ratios (m/z) down to the 3rd and 4th decimal place for metabolites less than a few thousand Daltons. This is accurate enough to distinguish relativistic mass differences between expected isotopes of CHONPS elements and unambiguously determine the isotope-specific molecular formula of an individual peak. Furthermore, the FT-ICR-MS's high mass resolution allows for the direct detection or deconvolution of individual isotopologues or mass-equivalent sets of isotopomers for a given metabolite.
Isotopologue identification and quantification of thousands of metabolites in these metabolomic experiments can provide a wealth of data for modeling the flux through metabolic networks. But before isotopologue intensity data can be properly interpreted, the contributions from isotopic natural abundance must be factored out (deisotoped). This is a computationally expensive and analytically intractable problem for data from lower mass resolution spectrometers where individual isotopically-resolved isotopologues cannot be distinguished . In these instances, numerical methods have been employed to approximate and subtract the contributions from isotopic natural abundance [4, 7–9]. Some of these calculations are aimed at a different deisotoping problem, namely identifying the related isotopologues and calculating the monoisotopic mass from its isotopic mass distribution [10, 11]. Fortuitously, with the isotope-resolved isotopologue peaks from FT-ICR-MS histograms, we can pose a similar but distinct problem that allows for the derivation of a computationally tractable analytical solution. In addition, isotopologues derived from the same molecule (or very similar set of molecules) neatly handle peak intensity referencing issues by providing a natural internal reference.
Derivation of the analytical solution
Equation 1 represents the relative distribution of carbon isotopologues from natural abundance only, as a sum of multinomial coefficients multiplied by the intensity of IM+0, the theoretically untainted 12C monoisotopic peak. The terms being summed are similar in form to those presented in Snider, 2007. IM+i;NA is the expected intensity of the ith isotopologue peak representing i additional nucleons. NAxC is the fractional natural abundance of the XC isotope. CMax is the number of carbons in the molecule. The multinomial coefficients, derived from the multinomial theorem with 3 variables represent the number of possible isotopomers of identical mass for a molecule with CMax carbons given 3 isotopes of carbon: 12C, 13C, and 14C.
Sequential correction of 13C natural abundance effects in a four-carbon example
IM+i=bValue = (cIM+i;NA- ΣIM+x*BC(x, i))/(1 - BCsum(i))
IM+0 = 1.00 = (0.956)/(1.00 - 4.36E-2)
IM+1 = 1.00 = (1.01 - 1.00 * 4.29E-2)/(1.00 - 3.29E-2)
IM+2 = 0.00 = (3.33E-2 - 1.00 * 7.22E-4 - 1.00 * 3.25E-2)/(1.00 - 2.21E-2)
IM+3 = 0.00 = (3.70E-4 - 1.00 * 5.40E-6 - 1.00 * 3.65E-4 - 0.00 * 2.19E-2)
/(1.00 - 1.11E-2)
IM+4 = 0.00 = (1.38E-6 - 1.00 * 1.51E-8 - 1.00 * 1.36E-6 - 0.00 * 1.23E-4
- 0.00 * 1.11E-2)/(1.00 - 0.00)
A version of each equation in larger fonts is available in Additional file 1.
Implementation of the algorithm
Testing the implementation
The implementation is also quite efficient even in an interpreted programming language like Perl. 10,000 repetitions of this algorithm for all 3 simulated test sets took only 17 seconds on a single core of an Intel T7200 Core 2 Duo mobile processor with 2GB of RAM and running release 5.3 of the RedHat Enterprise Linux operating system. The implementation is also very accurate. Given the perfect data in these three simulated test sets, the largest error was 4.12 × 10-16 seen in the IM+1 corrected intensity for the test set representing no 13C-labeling (Figure 2A). Furthermore, the implementation appears quite robust since the relative error actually decreases as the number of carbons (CMax) increases. At a CMax = 100, the relative error is 6.77 × 10-17. This implementation does have some numerical limitations, for example, the CMax must be less than 270 carbons due to all numerical quantities being represented as double precision (64 bit) floating point numbers. However, this limitation is easily overcome by using higher precision floating point numbers.
Application to phosphatidylcholine 34:1 observed isotopologue intensities
Discussion and Conclusions
Overall, correcting for the effects of natural abundance makes interpretation of isotopologue intensities from stable isotope tracing experiments easier within the context of cellular metabolism. Such a correction is required before using more quantitative methods of interpretation. Since the relative error is virtually zero with perfectly simulated data and the algorithm is very robust with increasing CMax, the accuracy of this correction is really only limited by the error in the isotopologue intensities themselves. Thus, the propagation of data error through this algorithm should be straightforward to analyze and quantify. Moreover, from Equation 5 it is evident that effects from natural abundance significantly link together groups of observed isotopologue intensities. This difference between calculated and observed intensities should be highly sensitive to the error in a set of isotopologue intensities. Therefore, this difference should be usable as an independent check on the quality of the observed set of isotopologue intensities. Such a quality control check would be especially useful when it is not possible or practical to repeat experiments or to determine whether additional experiments are necessary.
Cell Culture and FT-ICR-MS
We separated glycerophospholipids from crude cell extracts derived from MCF7-LCC2 cells in tissue culture after 24 hours of labeling with uniformly labeled 13C-glucose. We analyzed the sample on a hybrid linear ion trap 7T FT-ICR mass spectrometer (Finnigan LTQ FT, Thermo Electron, Bremen, Germany) equipped with a TriVersa NanoMate ion source (Advion BioSciences, Ithaca, NY) as described elsewhere .
Supported in part by NSF EPSCoR grant #EPS-0447479.
I thank Drs. T. W-M. Fan. A.N. Lane and R.M. Higashi for support and helpful discussion.
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