Construction of Confidence Regions for Isotopic Abundance Patterns in LC/MS Data Sets for Rigorous Determination of Molecular Formulas

It has long been recognized that estimates of isotopic abundance patterns may be instrumental in identifying the many unknown compounds encountered when conducting untargeted metabolic profiling using liquid chromatography/mass spectrometry. While numerous methods have been developed for assigning heuristic scores to rank the degree of fit of the observed abundance patterns with theoretical ones, little work has been done to quantify the errors that are associated with the measurements made. Thus, it is generally not possible to determine, in a statistically meaningful manner, whether a given chemical formula would likely be capable of producing the observed data. In this paper, we present a method for constructing confidence regions for the isotopic abundance patterns based on the fundamental distribution of the ion arrivals. Moreover, we develop a method for doing so that makes use of the information pooled together from the measurements obtained across an entire chromatographic peak, as well as from any adducts, dimers, and fragments observed in the mass spectra. This greatly increases the statistical power, thus enabling the analyst to rule out a potentially much larger number of candidate formulas while explicitly guarding against false positives. In practice, small departures from the model assumptions are possible due to detector saturation and interferences between adjacent isotopologues. While these factors form impediments to statistical rigor, they can to a large extent be overcome by restricting the analysis to moderate ion counts and by applying robust statistical methods. Using real metabolic data, we demonstrate that the method is capable of reducing the number of candidate formulas by a substantial amount, even when no bromine or chlorine atoms are present. We argue that further developments in our ability to characterize the data mathematically could enable much more powerful statistical analyses.