: The identification of small molecules from mass spectrometry (MS) data remains a major challenge in the interpretation of MS data. This review covers the computational aspects of identifying small molecules, from the identification of a compound searching a reference spectral library, to the structural elucidation of unknowns. In detail, we describe the basic principles and pitfalls of searching mass spectral reference libraries. Determining the molecular formula of the compound can serve as a basis for subsequent structural elucidation; consequently, we cover different methods for molecular formula identification, focussing on isotope pattern analysis. We then discuss automated methods to deal with mass spectra of compounds that are not present in spectral libraries, and provide an insight into de novo analysis of fragmentation spectra using fragmentation trees. In addition, this review shortly covers the reconstruction of metabolic networks using MS data. Finally, we list available software for different steps of the analysis pipeline.

We present results of the SIRIUS² submission to the 2012 CASMI contest. Only results for Category 1 (molecular formula identification) were submitted. The SIRIUS method and the parameters used are briefly described, followed by detailed analysis of the results and a discussion of cases where SIRIUS² was unable to come up with the correct molecular formula. SIRIUS² returns consistently high quality results, with the exception of fragmentation pattern analysis of time-of-flight data. We then discuss possibilities for further improving SIRIUS² in the future.

Since metabolites cannot be predicted from the genome sequence, high-throughput de novo identification of small molecules is highly sought. Mass spectrometry (MS) in combination with a fragmentation technique is commonly used for this task. Unfortunately, automated analysis of such data is in its infancy. Recently, fragmentation trees have been proposed as an analysis tool for such data. Additional fragmentation steps (MS ⁿ ) reveal more information about the molecule. We propose to use MS ⁿ data for the computation of fragmentation trees, and present the C olorful S ubtree C losure problem to formalize this task: There, we search for a colorful subtree inside a vertex-colored graph, such that the weight of the transitive closure of the subtree is maximal. We give several negative results regarding the tractability and approximability of this and related problems. We then present an exact dynamic programming algorithm, which is parameterized by the number of colors in the graph and is swift in practice. Evaluation of our method on a dataset of 45 reference compounds showed that the quality of constructed fragmentation trees is improved by using MS ⁿ instead of MS ² measurements.

For many years, copolymerization has been studied using mathematical and statistical models. Here, we present new Markov chain models for copolymerization kinetics: the Bernoulli and Geometric models. They model copolymer synthesis as a random process and are based on a basic reaction scheme. In contrast to previous Markov chain approaches to copolymerization, both models take variable chain lengths and time-dependent monomer probabilities into account and allow for computing sequence likelihoods and copolymer fingerprints. Fingerprints can be computed from copolymer mass spectra, potentially allowing us to estimate the model parameters from measured fingerprints. We compare both models against Monte Carlo simulations. We find that computing the models is fast and memory efficient.

The annotation of small molecules in untargeted mass spectrometry relies on the matching of fragment spectra to reference library spectra. While various spectrum-spectrum match scores exist, the field lacks statistical methods for estimating the false discovery rates (FDR) of these annotations. We present empirical Bayes and target-decoy based methods to estimate the false discovery rate. Relying on estimations of false discovery rates, we explore the effect of different spectrum-spectrum match criteria on the number and the nature of the molecules annotated. We show that the spectral matching settings needs to be adjusted for each project. By adjusting the scoring parameters and thresholds, the number of annotations rose, on average, by +139% (ranging from −92% up to +5705%) when compared to a default parameter set available at GNPS. The FDR estimation methods presented will enable a user to define the scoring criteria for large scale analysis of untargeted small molecule data that has been essential in the advancement of large scale proteomics, transcriptomics, and genomics science.

The geometric copolymerization model is a recently introduced statistical Markov chain model. Here, we investigate its practicality. First, several approaches to identify the optimal model parameters from observed copolymer fingerprints are evaluated using Monte Carlo simulated data. Directly optimizing the parameters is robust against noise but has impractically long running times. A compromise between robustness and running time is found by exploiting the relationship between monomer concentrations calculated by ordinary differential equations and the geometric model. Second, we investigate the applicability of the model to copolymerizations beyond living polymerization and show that the model is useful for copolymerizations involving termination and depropagation reactions.