The discovery and identification of molecules in biological and environmental samples is crucial for advancing biomedical and chemical sciences. Tandem mass spectrometry (MS/MS) is the leading technique for high-throughput elucidation of molecular structures. However, decoding a molecular structure from its mass spectrum is exceptionally challenging, even when performed by human experts. As a result, the vast majority of acquired MS/MS spectra remain uninterpreted, thereby limiting our understanding of the underlying (bio)chemical processes. Despite decades of progress in machine learning applications for predicting molecular structures from MS/MS spectra, the development of new methods is severely hindered by the lack of standard datasets and evaluation protocols. To address this problem, we propose MassSpecGym -- the first comprehensive benchmark for the discovery and identification of molecules from MS/MS data. Our benchmark comprises the largest publicly available collection of high-quality MS/MS spectra and defines three MS/MS annotation challenges: \textit{de novo} molecular structure generation, molecule retrieval, and spectrum simulation. It includes new evaluation metrics and a generalization-demanding data split, therefore standardizing the MS/MS annotation tasks and rendering the problem accessible to the broad machine learning community. MassSpecGym is publicly available at \url{https://github.com/pluskal-lab/MassSpecGym}.

In metabolomics, small molecules are structurally elucidated using tandem mass spectrometry (MS/MS); this computational task can be formulated as the Maximum Colorful Subtree problem, which is NP-hard. Unfortunately, data from a single metabolite requires us to solve hundreds or thousands of instances of this problem - and in a single Liquid Chromatography MS/MS run, hundreds or thousands of metabolites are measured. Here, we comprehensively evaluate the performance of several heuristic algorithms for the problem. Unfortunately, as is often the case in bioinformatics, the structure of the (chemically) true solution is not known to us; therefore we can only evaluate against the optimal solution of an instance. Evaluating the quality of a heuristic based on scores can be misleading: Even a slightly suboptimal solution can be structurally very different from the optimal solution, but it is the structure of a solution and not its score that is relevant for the downstream analysis. To this end, we propose a different evaluation setup: Given a set of candidate instances of which exactly one is known to be correct, the heuristic in question solves each instance to the best of its ability, producing a score for each instance, which is then used to rank the instances. We then evaluate whether the correct instance is ranked highly by the heuristic. We find that one particular heuristic consistently ranks the correct instance in a top position. We also find that the scores of the best heuristic solutions are very close to the optimal score; in contrast, the structure of the solutions can deviate significantly from the optimal structures. Integrating the heuristic allowed us to speed up computations in practice by a factor of 100-fold.

Motivation: Liquid Chromatography (LC) followed by tandem Mass Spectrometry (MS/MS) is one of the predominant methods for metabolite identification. In recent years, machine learning has started to transform the analysis of tandem mass spectra and the identification of small molecules. In contrast, LC data is rarely used to improve metabolite identification, despite numerous published methods for retention time prediction using machine learning. Results: We present a machine learning method for predicting the retention order of molecules; that is, the order in which molecules elute from the LC column. Our method has important advantages over previous approaches: We show that retention order is much better conserved between instruments than retention time. To this end, our method can be trained using retention time measurements from different LC systems and configurations without tedious pre-processing, significantly increasing the amount of available training data. Our experiments demonstrate that retention order prediction is an effective way to learn retention behaviour of molecules from heterogeneous retention time data. Finally, we demonstrate how retention order prediction and MS/MS-based scores can be combined for more accurate metabolite identifications when analyzing a complete LC-MS/MS run. Availability and implementation: Implementation of the method is available at https://version.aalto.fi/gitlab/bache1/retention_order_prediction.git.

Motivation: Metabolites, small molecules that are involved in cellular reactions, provide a direct functional signature of cellular state. Untargeted metabolomics experiments usually rely on tandem mass spectrometry to identify the thousands of compounds in a biological sample. Recently, we presented CSI:FingerID for searching in molecular structure databases using tandem mass spectrometry data. CSI:FingerID predicts a molecular fingerprint that encodes the structure of the query compound, then uses this to search a molecular structure database such as PubChem. Scoring of the predicted query fingerprint and deterministic target fingerprints is carried out assuming independence between the molecular properties constituting the fingerprint. Results: We present a scoring that takes into account dependencies between molecular properties. As before, we predict posterior probabilities of molecular properties using machine learning. Dependencies between molecular properties are modeled as a Bayesian tree network; the tree structure is estimated on the fly from the instance data. For each edge, we also estimate the expected covariance between the two random variables. For fixed marginal probabilities, we then estimate conditional probabilities using the known covariance. Now, the corrected posterior probability of each candidate can be computed, and candidates are ranked by this score. Modeling dependencies improves identification rates of CSI:FingerID by 2.85 percentage points. Availability and implementation: The new scoring Bayesian (fixed tree) is integrated into SIRIUS 4.0 (https://bio.informatik.uni-jena.de/software/sirius/).

In this paper, we present a novel method for solving structured prediction problems, based on combining Input Output Kernel Regression (IOKR) with an extension of magnitude-preserving ranking to structured output spaces. In particular, we concentrate on the case where a set of candidate outputs has been given, and the associated pre-image problem calls for ranking the set of candidate outputs. Our method, called magnitude-preserving IOKR, both aims to produce a good approximation of the output feature vectors, and to preserve the magnitude differences of the output features in the candidate sets. For the case where the candidate set does not contain corresponding ’correct’ inputs, we propose a method for approximating the inputs through application of IOKR in the reverse direction. We apply our method to two learning problems: cross-lingual document retrieval and metabolite identification. Experiments show that the proposed approach improves performance over IOKR, and in the latter application obtains the current state-of-the-art accuracy.

MOTIVATION: An important problematic of metabolomics is to identify metabolites using tandem mass spectrometry data. Machine learning methods have been proposed recently to solve this problem by predicting molecular fingerprint vectors and matching these fingerprints against existing molecular structure databases. In this work we propose to address the metabolite identification problem using a structured output prediction approach. This type of approach is not limited to vector output space and can handle structured output space such as the molecule space. RESULTS: We use the Input Output Kernel Regression method to learn the mapping between tandem mass spectra and molecular structures. The principle of this method is to encode the similarities in the input (spectra) space and the similarities in the output (molecule) space using two kernel functions. This method approximates the spectra-molecule mapping in two phases. The first phase corresponds to a regression problem from the input space to the feature space associated to the output kernel. The second phase is a preimage problem, consisting in mapping back the predicted output feature vectors to the molecule space. We show that our approach achieves state-of-the-art accuracy in metabolite identification. Moreover, our method has the advantage of decreasing the running times for the training step and the test step by several orders of magnitude over the preceding methods. CONTACT: [email protected] SUPPLEMENTARY INFORMATION: Supplementary data are available at Bioinformatics online.

We outline a blueprint for the development of new computer science approaches for the management and analysis of big data problems for biodiversity science. Such problems are characterized by a combination of different data sources each of which owns at least one of the typical characteristics of big data (volume, variety, velocity, or veracity). For these problems, we envision a solution that covers different aspects of integrating data sources and algorithms for their analysis on one of the following three layers: At the data layer, there are various data archives of heterogeneous, unstructured, and uncertain data. At the functional layer, the data are analyzed for each archive individually. At the meta-layer, multiple functional archives are combined for complex analysis.

MOTIVATION: Metabolite identification from tandem mass spectrometric data is a key task in metabolomics. Various computational methods have been proposed for the identification of metabolites from tandem mass spectra. Fragmentation tree methods explore the space of possible ways in which the metabolite can fragment, and base the metabolite identification on scoring of these fragmentation trees. Machine learning methods have been used to map mass spectra to molecular fingerprints; predicted fingerprints, in turn, can be used to score candidate molecular structures. RESULTS: Here, we combine fragmentation tree computations with kernel-based machine learning to predict molecular fingerprints and identify molecular structures. We introduce a family of kernels capturing the similarity of fragmentation trees, and combine these kernels using recently proposed multiple kernel learning approaches. Experiments on two large reference datasets show that the new methods significantly improve molecular fingerprint prediction accuracy. These improvements result in better metabolite identification, doubling the number of metabolites ranked at the top position of the candidates list.

BACKGROUND: Genes occurring co-localized in multiple genomes can be strong indicators for either functional constraints on the genome organization or remnant ancestral gene order. The computational detection of these patterns, which are usually referred to as gene clusters, has become increasingly sensitive over the past decade. The most powerful approaches allow for various types of imperfect cluster conservation: Cluster locations may be internally rearranged. The individual cluster locations may contain only a subset of the cluster genes and may be disrupted by uninvolved genes. Moreover cluster locations may not at all occur in some or even most of the studied genomes. The detection of such low quality clusters increases the risk of mistaking faint patterns that occur merely by chance for genuine findings. Therefore, it is crucial to estimate the significance of computational gene cluster predictions and discriminate between true conservation and coincidental clustering. RESULTS: In this paper, we present an efficient and accurate approach to estimate the significance of gene cluster predictions under the approximate common intervals model. Given a single gene cluster prediction, we calculate the probability to observe it with the same or a higher degree of conservation under the null hypothesis of random gene order, and add a correction factor to account for multiple testing. Our approach considers all parameters that define the quality of gene cluster conservation: the number of genomes in which the cluster occurs, the number of involved genes, the degree of conservation in the different genomes, as well as the frequency of the clustered genes within each genome. We apply our approach to evaluate gene cluster predictions in a large set of well annotated genomes.

MOTIVATION: Mass spectrometry allows sensitive, automated and high-throughput analysis of small molecules such as metabolites. One major bottleneck in metabolomics is the identification of 'unknown' small molecules not in any database. Recently, fragmentation tree alignments have been introduced for the automated comparison of the fragmentation patterns of small molecules. Fragmentation pattern similarities are strongly correlated with the chemical similarity of the molecules, and allow us to cluster compounds based solely on their fragmentation patterns. RESULTS: Aligning fragmentation trees is computationally hard. Nevertheless, we present three exact algorithms for the problem: a dynamic programming (DP) algorithm, a sparse variant of the DP, and an Integer Linear Program (ILP). Evaluation of our methods on three different datasets showed that thousands of alignments can be computed in a matter of minutes using DP, even for 'challenging' instances. Running times of the sparse DP were an order of magnitude better than for the classical DP. The ILP was clearly outperformed by both DP approaches. We also found that for both DP algorithms, computing the 1% slowest alignments required as much time as computing the 99% fastest.

In computational phylogenetics, the problem of constructing a consensus tree for a given set of rooted input trees has frequently been addressed. In this article we study the Minimum-Flip Problem : the input trees are transformed into a binary matrix, and we want to find a perfect phylogeny for this matrix using a minimum number of flips, that is, corrections of single entries in the matrix. The graph-theoretical formulation of the problem is as follows: Given a bipartite graph G = ( Vt ∪ Vc , E ), the task is to find a minimum set of edge modifications such that the resulting graph has no induced path with four edges that starts and ends in Vt , where Vt corresponds to the taxa set and Vc corresponds to the character set. We present two fixed-parameter algorithms for the Minimum-Flip Problem , one with running time O (4.83 k + poly ( m , n )) and another one with running time O (4.42 k + poly ( m , n )) for n taxa, m characters, k flips, and poly ( m , n ) denotes a polynomial function in m and n . Additionally, we discuss several heuristic improvements. We also report computational results on phylogenetic data.

Let S be a set of k strings over an alphabet Σ; each string has a length between ℓ and n. The Closest Substring Problem (CSSP) is to find a minimal integer d (and a corresponding string t of length ℓ) such that each string s ∊ S has a substring of length ℓ with Hamming distance at most d to t. We say t is the closest substring to S. For ℓ = n, this problem is known as the Closest String Problem (CSP). Particularly in computational biology, the CSP and CSSP have found numerous practical applications such as identifying regulatory motifs and approximate gene clusters, and in degenerate primer design. We study ILP formulations for both problems. Our experiments show that a position-based formulation for the CSP performs very well on real-world instances emerging from biology. Even on randomly generated instances that are hard to solve to optimality, solving the root relaxation leads to solutions very close to the optimum. For the CSSP we give a new formulation that is polytope-wise stronger than a straightforward extension of the CSP formulation. Furthermore we propose a strengthening constraint class that speeds up the running time.

MOTIVATION: Numerous applications in Computational Biology process molecular structures and hence strongly rely not only on correct atomic coordinates but also on correct bond order information. For proteins and nucleic acids, bond orders can be easily deduced but this does not hold for other types of molecules like ligands. For ligands, bond order information is not always provided in molecular databases and thus a variety of approaches tackling this problem have been developed. In this work, we extend an ansatz proposed by Wang et al. that assigns connectivity-based penalty scores and tries to heuristically approximate its optimum. In this work, we present three efficient and exact solvers for the problem replacing the heuristic approximation scheme of the original approach: an A*, an ILP and an fixed-parameter approach (FPT) approach. RESULTS: We implemented and evaluated the original implementation, our A*, ILP and FPT formulation on the MMFF94 validation suite and the KEGG Drug database. We show the benefit of computing exact solutions of the penalty minimization problem and the additional gain when computing all optimal (or even suboptimal) solutions. We close with a detailed comparison of our methods. AVAILABILITY: The A* and ILP solution are integrated into the open-source C++ LGPL library BALL and the molecular visualization and modelling tool BALLView and can be downloaded from our homepage www.ball-project.org. The FPT implementation can be downloaded from http://bio.informatik.uni-jena.de/software/.

BACKGROUND: The center string (or closest string) problem is a classic computer science problem with important applications in computational biology. Given k input strings and a distance threshold d, we search for a string within Hamming distance at most d to each input string. This problem is NP complete. RESULTS: In this paper, we focus on exact methods for the problem that are also swift in application. We first introduce data reduction techniques that allow us to infer that certain instances have no solution, or that a center string must satisfy certain conditions. We describe how to use this information to speed up two previously published search tree algorithms. Then, we describe a novel iterative search strategy that is efficient in practice, where some of our reduction techniques can also be applied. Finally, we present results of an evaluation study for two different data sets from a biological application. CONCLUSIONS: We find that the running time for computing the optimal center string is dominated by the subroutine calls for d = dopt -1 and d = dopt. Our data reduction is very effective for both, either rejecting unsolvable instances or solving trivial positions. We find that this speeds up computations considerably.

Glycans are molecules made from simple sugars that form complex tree structures. Glycans constitute one of the most important protein modifications and identification of glycans remains a pressing problem in biology. Unfortunately, the structure of glycans is hard to predict from the genome sequence of an organism. In this paper, we consider the problem of deriving the topology of a glycan solely from tandem mass spectrometry (MS) data. We study, how to generate glycan tree candidates that sufficiently match the sample mass spectrum, avoiding the combinatorial explosion of glycan structures. Unfortunately, the resulting problem is known to be computationally hard. We present an efficient exact algorithm for this problem based on fixed-parameter algorithmics that can process a spectrum in a matter of seconds. We also report some preliminary results of our method on experimental data, combining it with a preliminary candidate evaluation scheme. We show that our approach is fast in applications, and that we can reach very well de novo identification results. Finally, we show how to count the number of glycan topologies for a fixed size or a fixed mass. We generalize this result to count the number of (labeled) trees with bounded out degree, improving on results obtained using Pólya's enumeration theorem.

Abstract Motivation: High-resolution mass spectrometry (MS) is among the most widely used technologies in metabolomics. Metabolites participate in almost all cellular processes, but most metabolites still remain uncharacterized. Determination of the sum formula is a crucial step in the identification of an unknown metabolite, as it reduces its possible structures to a hopefully manageable set. Results: We present a method for determining the sum formula of a metabolite solely from its mass and the natural distribution of its isotopes. Our input is a measured isotope pattern from a high resolution mass spectrometer, and we want to find those molecules that best match this pattern. Our method is computationally efficient, and results on experimental data are very promising: for orthogonal time-of-flight mass spectrometry, we correctly identify sum formulas for >90% of the molecules, ranging in mass up to 1000 Da. Availability: SIRIUS is available under the LGPL license at http://bio.informatik.uni-jena.de/sirius/ Contact: [email protected] Supplementary information: Supplementary data are available at Bioinformatics online.

BACKGROUND: The COMPARABILITY EDITING problem appears in the context of hierarchical disease classification based on noisy data. We are given a directed graph G representing hierarchical relationships between patient subgroups. The task is to identify the minimum number of edge insertions or deletions to transform G into a transitive graph, that is, if edges (u, v) and (v, w) are present then edge (u, w) must be present, too. RESULTS: We present two new approaches for the problem based on fixed-parameter algorithmics and integer linear programming. In contrast to previously used heuristics, our approaches compute provably optimal solutions. CONCLUSION: Our computational results demonstrate that our exact algorithms are by far more efficient in practice than a previously used heuristic approach. In addition to the superior running time performance, our algorithms are capable of enumerating all optimal solutions, and naturally solve the weighted version of the problem.

UNLABELLED: We introduce Decomp, a tool that computes the sum formula of all molecules whose mass equals the input mass. This problem arises frequently in biochemistry and mass spectrometry (MS), when we know the molecular mass of a protein, DNA or metabolite fragment but have no other information. A closely related problem is known as the Money Changing Problem (MCP), where all masses are positive integers. Recently, efficient algorithms have been developed for the MCP, in which Decomp applies to real-valued MS data. The excellent performance of this method on proteomic and metabolomic MS data has recently been demonstrated. Decomp has an easy-to-use graphical interface, which caters for both types of users: those interested in solving MCP instances and those submitting MS data. AVAILABILITY: Decomp is freely accessible at http://bibiserv.techfak.uni-bielefeld.de/decomp/.

Abstract Summary: Estimating Phylogenies of Species (EPoS) is a modular software framework for phylogenetic analysis, visualization and data management. It provides a plugin-based system that integrates a storage facility, a rich user interface and the ability to easily incorporate new methods, functions and visualizations. EPoS ships with persistent data management, a set of well-known phylogenetic algorithms and a multitude of tree visualization methods and layouts. Implemented algorithms cover distance-based tree construction, consensus trees and various graph-based supertree methods. The rendering system can be customized for, say, different edge and node styles. Availability: Executables and source code are available under the LGPL license at http://www.bio.informatik.uni-jena.de/epos. Contact: [email protected] Supplementary information: The homepage contains tutorials and documentation for both users and programmers who want to develop plugins and extensions.

BACKGROUND: Mass spectrometry is a key technique in proteomics and can be used to analyze complex samples quickly. One key problem with the mass spectrometric analysis of peptides and proteins, however, is the fact that absolute quantification is severely hampered by the unclear relationship between the observed peak intensity and the peptide concentration in the sample. While there are numerous approaches to circumvent this problem experimentally (e.g. labeling techniques), reliable prediction of the peak intensities from peptide sequences could provide a peptide-specific correction factor. Thus, it would be a valuable tool towards label-free absolute quantification. RESULTS: In this work we present machine learning techniques for peak intensity prediction for MALDI mass spectra. Features encoding the peptides' physico-chemical properties as well as string-based features were extracted. A feature subset was obtained from multiple forward feature selections on the extracted features. Based on these features, two advanced machine learning methods (support vector regression and local linear maps) are shown to yield good results for this problem (Pearson correlation of 0.68 in a ten-fold cross validation). CONCLUSION: The techniques presented here are a useful first step going beyond the binary prediction of proteotypic peptides towards a more quantitative prediction of peak intensities. These predictions in turn will turn out to be beneficial for mass spectrometry-based quantitative proteomics.

Mass spectrometry has become one of the most popular analysis techniques in Proteomics and Systems Biology. With the creation of larger datasets, the automated recalibration of mass spectra becomes important to ensure that every peak in the sample spectrum is correctly assigned to some peptide and protein. Algorithms for recalibrating mass spectra have to be robust with respect to wrongly assigned peaks, as well as efficient due to the amount of mass spectrometry data. The recalibration of mass spectra leads us to the problem of finding an optimal matching between mass spectra under measurement errors. We have developed two deterministic methods that allow robust computation of such a matching: The first approach uses a computational geometry interpretation of the problem, and tries to find two parallel lines with constant distance that stab a maximal number of points in the plane. The second approach is based on finding a maximal common approximate subsequence, and improves existing algorithms by one order of magnitude exploiting the sequential nature of the matching problem. We compare our results to a computational geometry algorithm using a topological line-sweep.

MOTIVATION: Single Nucleotide Polymorphisms (SNPs) are believed to contribute strongly to the genetic variability in living beings, and SNP and mutation discovery are of great interest in today's Life Sciences. A comparatively new method to discover such polymorphisms is based on base-specific cleavage, where resulting cleavage products are analyzed by mass spectrometry (MS). One particular advantage of this method is the possibility of multiplexing the biochemical reactions, i.e. examining multiple genomic regions in parallel. Simulations can help estimating the performance of a method for polymorphism discovery, and allow us to evaluate the influence of method parameters on the discovery rate, and also to investigate whether the method is well suited for a certain genomic region. RESULTS: We show how to efficiently conduct such simulations for polymorphism discovery using base-specific cleavage and MS. Simulating multiplexed polymorphism discovery leads us to the problem of uniformly drawing a multiplex. Given a multiset of natural numbers we want to uniformly draw a subset of fixed cardinality so that the elements sum up to some fixed total length. We show how to enumerate multiplex layouts using dynamic programming, which allows us to uniformly draw a multiplex.

BACKGROUND: Mass spectrometry based peptide mass fingerprints (PMFs) offer a fast, efficient, and robust method for protein identification. A protein is digested (usually by trypsin) and its mass spectrum is compared to simulated spectra for protein sequences in a database. However, existing tools for analyzing PMFs often suffer from missing or heuristic analysis of the significance of search results and insufficient handling of missing and additional peaks. RESULTS: We present an unified framework for analyzing Peptide Mass Fingerprints that offers a number of advantages over existing methods: First, comparison of mass spectra is based on a scoring function that can be custom-designed for certain applications and explicitly takes missing and additional peaks into account. The method is able to simulate almost every additive scoring scheme. Second, we present an efficient deterministic method for assessing the significance of a protein hit, independent of the underlying scoring function and sequence database. We prove the applicability of our approach using biological mass spectrometry data and compare our results to the standard software Mascot. CONCLUSION: The proposed framework for analyzing Peptide Mass Fingerprints shows performance comparable to Mascot on small peak lists. Introducing more noise peaks, we are able to keep identification rates at a similar level by using the flexibility introduced by scoring schemes.