Fragmentation Trees Research Articles

Computational mass spectrometry for small molecules.

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.

General fragmentation trees

We show that the genealogy of any self-similar fragmentation process can be encoded in a compact measured real tree. Under some Malthusian hypotheses, we compute the fractal Hausdorff dimension of this tree through the use of a natural measure on the set of its leaves. This generalizes previous work of Haas and Miermont which was restricted to conservative fragmentation processes.

Consistent Markov branching trees with discrete edge lengths

We study consistent collections of random fragmentation trees with random integer-valued edge lengths. We prove several equivalent necessary and sufficient conditions under which Geometrically distributed edge lengths can be consistently assigned to a Markov branching tree. Among these conditions is a characterization by a unique probability measure, which plays a role similar to the dislocation measure for homogeneous fragmentation processes. We discuss this and other connections to previous work on Markov branching trees and homogeneous fragmentation processes.

Fragmentation trees for the structural characterisation of metabolites.

Metabolite identification plays a crucial role in the interpretation of metabolomics research results. Due to its sensitivity and widespread implementation, a favourite analytical method used in metabolomics is electrospray mass spectrometry. In this paper, we demonstrate our results in attempting to incorporate the potentials of multistage mass spectrometry into the metabolite identification routine. New software tools were developed and implemented which facilitate the analysis of multistage mass spectra and allow for efficient removal of spectral artefacts. The pre-processed fragmentation patterns are saved as fragmentation trees. Fragmentation trees are characteristic of molecular structure. We demonstrate the reproducibility and robustness of the acquisition of such trees on a model compound. The specificity of fragmentation trees allows for distinguishing structural isomers, as shown on a pair of isomeric prostaglandins. This approach to the analysis of the multistage mass spectral characterisation of compounds is an important step towards formulating a generic metabolite identification method. Copyright © 2012 John Wiley & Sons, Ltd.

MetiTree: a web application to organize and process high-resolution multi-stage mass spectrometry metabolomics data

Summary: Identification of metabolites using high-resolution multi-stage mass spectrometry (MSn) data is a significant challenge demanding access to all sorts of computational infrastructures. MetiTree is a user-friendly, web application dedicated to organize, process, share, visualize and compare MSn data. It integrates several features to export and visualize complex MSn data, facilitating the exploration and interpretation of metabolomics experiments. A dedicated spectral tree viewer allows the simultaneous presentation of three related types of MSn data, namely, the spectral data, the fragmentation tree and the fragmentation reactions. MetiTree stores the data in an internal database to enable searching for similar fragmentation trees and matching against other MSn data. As such MetiTree contains much functionality that will make the difficult task of identifying unknown metabolites much easier.Availability: MetiTree is accessible at http://www.MetiTree.nl. The source code is available at https://github.com/NetherlandsMetabolomicsCentre/metitree/wiki.Contact: m.rojas@lacdr.leidenuniv.nl or t.reijmers@lacdr.leidenuniv.nl

De novo analysis of electron impact mass spectra using fragmentation trees

The automated fragmentation analysis of high resolution EI mass spectra based on a fragmentation tree algorithm is introduced. Fragmentation trees are constructed from EI spectra by automated signal extraction and evaluation. These trees explain relevant fragmentation reactions and assign molecular formulas to fragments. The method enables the identification of the molecular ion and the molecular formula of a metabolite if the molecular ion is present in the spectrum. These identifications are independent of existing library knowledge and, thus, support assignment and structural elucidation of unknown compounds. The method works even if the molecular ion is of very low abundance or hidden under contaminants with higher masses. We apply the algorithm to a selection of 50 derivatized and underivatized metabolites and demonstrate that in 78% of cases the molecular ion can be correctly assigned. The automatically constructed fragmentation trees correspond very well to published mechanisms and allow the assignment of specific relevant fragments and fragmentation pathways even in the most complex EI-spectra in our dataset. This method will be very helpful in the automated analysis of metabolites that are not included in common libraries and it thus has the potential to support the explorative character of metabolomics studies.

Metabolite Identification Using Automated Comparison of High-Resolution Multistage Mass Spectral Trees

Multistage mass spectrometry (MS(n)) generating so-called spectral trees is a powerful tool in the annotation and structural elucidation of metabolites and is increasingly used in the area of accurate mass LC/MS-based metabolomics to identify unknown, but biologically relevant, compounds. As a consequence, there is a growing need for computational tools specifically designed for the processing and interpretation of MS(n) data. Here, we present a novel approach to represent and calculate the similarity between high-resolution mass spectral fragmentation trees. This approach can be used to query multiple-stage mass spectra in MS spectral libraries. Additionally the method can be used to calculate structure-spectrum correlations and potentially deduce substructures from spectra of unknown compounds. The approach was tested using two different spectral libraries composed of either human or plant metabolites which currently contain 872 MS(n) spectra acquired from 549 metabolites using Orbitrap FTMS(n). For validation purposes, for 282 of these 549 metabolites, 765 additional replicate MS(n) spectra acquired with the same instrument were used. Both the dereplication and de novo identification functionalities of the comparison approach are discussed. This novel MS(n) spectral processing and comparison approach increases the probability to assign the correct identity to an experimentally obtained fragmentation tree. Ultimately, this tool may pave the way for constructing and populating large MS(n) spectral libraries that can be used for searching and matching experimental MS(n) spectra for annotation and structural elucidation of unknown metabolites detected in untargeted metabolomics studies.

Fast alignment of fragmentation trees.

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.Contact: sebastian.boecker@uni-jena.de

Fragment size and local flower density influence seed set of the understorey tree Paypayrola blanchetiana (Violaceae) in Brazilian Atlantic rain forest

Abstract:Reproductive success of many plant species declines in fragmented habitat, but this effect is little studied in trees of tropical rain forest understorey. Paypayrola blanchetiana (Violaceae) is a continuous-flowering treelet endemic to the Atlantic rain forest of north-east Brazil. Plants are distributed in localized patches. Flower, fruit and seed production of a total of 86 trees was quantified in six forest fragments, each belonging to one of two categories of size (> 300 ha vs. < 50 ha) and fragmentation history (isolated for c. 25–30 y vs. at least c. 50 y). Relative fruit set (fruits/flower) and seed set (seeds/ovule) were calculated for a spatial (total fruit set of tree individuals) and a temporal analysis (combined month-by-month fruit set in patches in response to different flowering intensities). Fruit set (1%) and seed set (0.6%) were very low, but variable among trees. Plants in large fragments had significantly higher fruit set and seed set than plants in small fragments. Trees in older fragments, however, displayed similar fruit and seed set to those in recently created ones. We found no interaction effect on seed set of fragment size and isolation time. Seed set was a negative function of patch flower density. Possible drivers of the observed patterns are discussed.

Identifying the Unknowns by Aligning Fragmentation Trees

Mass spectrometry allows sensitive, automated, and high-throughput analysis of small molecules. In principle, tandem mass spectrometry allows us to identify "unknown" small molecules not in any database, but the automated interpretation of such data is in its infancy. Fragmentation trees have recently been introduced for the automated analysis of the fragmentation patterns of small molecules. We present a method for the automated comparison of such fragmentation patterns, based on aligning the compounds' fragmentation trees. We cluster compounds based solely on their fragmentation patterns and show a good agreement with known compound classes. Fragmentation pattern similarities are strongly correlated with the chemical similarity of molecules. We present a tool for searching a database for compounds with fragmentation pattern similar to an unknown sample compound. We apply this tool to metabolites from Icelandic poppy. Our method allows fully automated computational identification of small molecules that cannot be found in any database.

Protected Apes, Unprotected Forest: Composition, Structure and Diversity of Riverine Forest Fragments and Their Conservation Value in Uganda

Small forest fragments are common in anthropogenic landscapes in the tropics. These have conservation value if they provide habitat for threatened wildlife and maintain connectivity between larger habitats. Riverine forests have particular ‘corridor’ potential due to their linear shape, but are under-studied in many regions. We surveyed trees in riverine fragments in Bulindi, an anthropogenic landscape 25 km south of the Budongo Forest in western Uganda, to determine their condition and assess their value for wildlife, particularly endangered chimpanzees Pan troglodytes. We assessed tree composition, structure and diversity and compared results with a previous survey made in Budongo, the nearest main forest block. Riverine fragments were considerably less species-dense and species-rich than Budongo. Community composition differed markedly between sites and there was virtually no overlap in common species. Common trees in fragments were characteristic of East African swamp and groundwater forests (e.g. the palm Phoenix reclinata) and the dominant tree family was the Moraceae, members of which produce fleshy fruits attractive to frugivores (e.g. figs). Important fruit foods for chimpanzees differed between habitats. While basal area of important fruit trees was comparable, overall density was greater in fragments. Our data suggest the riverine fragments offer a relatively food-dense habitat for chimpanzees and other frugivores. Small riverine forests have little or no protection regionally and are being extensively logged and cleared for agriculture. Species logged for timber in Bulindi included important chimpanzee fruit trees. Unless conservation projects successfully reverse current trends, the value of the riverine corridors for maintaining connectivity between main forest blocks is limited.

Is top‐down control by predators driving insect abundance and herbivory rates in fragmented forests?

AbstractThe effects of forest fragmentation on ecological interactions and particularly on food webs have scarcely been analysed. There is usually less herbivory in forest fragments than in continuous forests. Here we hypothesize that forest fragmentation enhances top‐down control of herbivory through an increase in insectivorous birds and a decrease in herbivorous insects, with a consequent decrease in plant reproductive success in small forest fragments. In the Maulino forest in central Chile, we experimentally excluded birds from Aristotelia chilensis (Elaeocarpaceae) trees in both forest fragments and continuous forest, and analysed herbivore insect abundance, herbivory and plant reproductive success during two consecutive growing seasons. We expected that insect abundance and herbivory would increase, and reproductive success would decrease in A. chilensis from which birds have been excluded, particularly in forest fragments where bird abundance and predation pressure on insects is higher. The abundance of herbivorous insects was lower in the forest fragments than in the continuous forest only in the first season, and herbivory was lower in forest fragments than in the continuous forest throughout the study. Moreover, during the second growing season herbivory was greater in the excluded trees than in the control trees, and as expected, there was a greater difference in the fragments than in the continuous forest, but this was not statistically significant. Exclusion of birds did not affect the reproductive success of A. chilensis. Our results, after 2 years of study, demonstrate that birds affect the levels of herbivory on A. chilensis in the Maulino forest, but do not support our hypothesis of enhanced top‐down control in fragmented forests, as the strength of the effect of excluding birds did not vary with fragmentation.

Vegetation status on Nishi-jima Island (Ogasawara) before eradication of alien herbivore mammals: rapid expansion of an invasive alien tree, Casuarina equisetifolia (Casuarinaceae)

Insular ecosystems can be dramatically affected by alien species, and records of pre-eradication status are essential to evaluate the effects of eradicating alien species. Nishi-jima Island is a small island of the Ogasawara group on which the first program of complete eradication of alien herbivorous mammals (black rats and feral goats) will be conducted. After eradication, the government plans to conduct ecosystem restoration on the island. This paper reports the angiosperm flora and vegetation of Nishi-jima Island before eradication of the rats and goats, with the objective of aiding ecosystem management after the eradication. Our surveys indicate that vegetation cover by the alien tree, Casuarina equisetifolia has expanded compared with its distribution in a 1974 aerial photograph of the island. The predominant vegetation in 2006 was C. equisetifolia forests and Zoysia tenuifolia grasslands, with fragmented native tree vegetation. The flora of the island comprised 69 angiosperm species (50 indigenous species) of which 30% were endemic, far less than for the Ogasawara Islands as a whole (45%). However, several populations of endangered plants remain. To restore the native ecosystem on Nishi-jima, eradication of C. equisetifolia is important in addition to eradication of alien herbivorous mammals.

Computing Fragmentation Trees from Metabolite Multiple Mass Spectrometry Data

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 Colorful Subtree Closure 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 MS² measurements.

Genetic diversity and divergence applied to Enviromental services for Araucaria angustifolia(Brazil)

Humans derive many utilitarian benefits from the environmental services of biotas and ecosystems.Yet ecosystem, species and genetic levels is increasingly lost from agricultural landscapes mainly due to maximisation of production [1,2]. The genetic variability is a result of several forces including mutation, recombination and gene flow. Allele frequencies are altered by natural selection and by genetic drift. Whilst mutation, recombination and genetic drift are random and independent processes, natural selection is a directional process towards evolutionary change [3]. The Araucaria Rainforest is one of the most important biomes occurring naturally in southern Brazil. The extensive logging and agricultural expansion became this forest extremely fragmented. Particularly important is the factor of ecosystem resilience, which appears to underpin many of the services. While biodiversity often plays a key role, the services can also derive from biomass and other attributes of biotas, for example, genetic diversity of a particular species. Landscape genetics are being used in this project to improve the understanding of fragmentation impact to assist an environmental services scheme. The objective of this study was to assess by microsatellites markers, the genetic diversity and dynamics in remnant patches of Araucaria angustifolia rainforest, with different levels of human modification. The project compared two different forest conditions: one is 1.157,48 ha of continuous forest, and the other is a fragmented forest remnant, with size from 8 ha, appraised 5 km from the continuous forest area. Genetic diversity and divergence of seedlings and adult individuals present in forest fragment was compared with the genetic composition of samples appraised in continuous forest. Cambium and seed material were collected from each recorded tree, and genomic DNA was extracted using the method described in Mazza & Bittencourt (2000). The seeds for DNA extraction had undergone a slight adjustment – Proteinase K was added to megagametophyte (maternal origin) and embryo extraction. Polymerase chain reaction (PCR) conditions used were establish by Qiagen Multiplex Master Mix protocol (1022830) and use fluorescents dye labelling. Two multiplexed systems of microsatellites were applied with the 8 primers. The eight loci used were CRCAc2, Ag23, Ag62, Ag45, CRCAc1, Ag20, Ag56 and As90. Following PCR this dilution was running in ABI sequencer 3100. Gene Scan and Genotyper software were used for data collection and alleles analysis. The average number of alleles per locus among adult trees in the continuous forest was 8.10, compared to 5.15 appraised in forest fragment. The means of expected heterozygosity were 0.623 for continuous forest and 0.579 for forest fragment, while observed heterozygosity range was respectively, 0.571 and 0.723. Subpopulations of forest fragments were more distinguished than subpopulations of continuous, due the average fixation index was 0.082 for subpopulations in the continuous forest and 0.210 in fragment. It is worth noting that the levels of genetic differentiation among all subpopulations can be considered to be high. Paternity analysis, within the continuous forest indicated that 48% of offspring were fertilized by pollen from trees outside the plot site. The average pollination distance within the continuous was 95 m. In the trees from forest fragment, the analysis showed that 42% to 65% of the offspring was fertilized by pollen from trees outside fragment. The effective number of pollen donors in the continuous forest ranged among seed-trees from 2 to 10, and in the fragment from 2 to 6. The results suggest high pollen dispersal distance in both conditions and an absence of reproductive isolation. They also show high pollen immigration and dispersal distance among the tree groups. The results suggest that fragmentation increases divergence in Araucaria angustifolia.The population in continuous forest showed higher genetic diversity in the adult population than the population of trees in fragment. The reducing the heterozygosity were low, may be due the recent forest fragmentation history. There are more inbreeding in fragmented population than in continuous population. Fragmentation increased the genetic divergence among the fragmented population. However, the genetic results indicated the presence of long-distance dispersal leading to functional connectivity between isolated forest fragment. The survival of remnants of Araucaria angustifolia patches as well as single trees in the agricultural landscape is key factors for species conservation and could be applied to environmental payment services, these strategy for A. angustifolia is an integration of conservation strategies across reserves and the surrounding matrix, including productive agricultural areas, to assist gene flow movement between temporally suitable habitats.

Analytic and numerical analysis of some statistical features of fragmentation processes

In this work, we investigate the following inhomogeneous model of fragmentation with an exponential splitting probability: suppose that an initial particle having a mass x 0 > 0 (large enough) is broken, with a size-dependent probability p ( x 0 ) ≔ 1 − e − x 0 , into b > 1 pieces. With probability 1 − p ( x 0 ) , this fragment is left unchanged for ever. The process of fragmentation is repeated recursively for all pieces. Some statistical features are studied, chiefly the fragment size distribution, number of fragments and partition function of the random fragmentation tree. Also, we give details of the numerical analysis of these features.

Correction to Computing Fragmentation Trees from Tandem Mass Spectrometry Data

Correction to Computing Fragmentation Trees from Tandem Mass Spectrometry Data

CID of singly charged antioxidants applied in lubricants by means of a 3D ion trap and a linear ion trap–Orbitrap mass spectrometer

The aim of this study was to investigate the fragmentation behavior induced by low-energy collision-induced dissociation (LE-CID) of four selected antioxidants applied in lubricants, by two different types of ion trap mass spectrometers: a three-dimensional ion trap (3D-IT) and a linear IT (LIT) Orbitrap MS. Two sterically hindered phenols and two aromatic amines were selected as model compounds representing different antioxidant classes and were characterized by positive-ion electrospray ionization (ESI) and LE-CID. Various types of molecular ions (e.g. [M](+•) , [M + H](+) , [M + NH(4) ](+) or [M + Na](+) ) were used as precursor ions generating a significant number of structurally relevant product ions. Furthermore, the phenolic compounds were analyzed by negative-ion ESI. For both IT types applied for fragmentation, the antioxidants exhibited the same unusual LE-CID behavior: (1) they formed stable radical product ions and (2) CC bond cleavages of aliphatic substituents were observed and their respective cleavage sites depended on the precursor ion selected. This fragmentation provided information on the type of structural isomer usually not obtainable for branched aliphatic substituents utilizing LE-CID. Comparing the two instruments, the main benefit of applying the LIT-Orbitrap was direct access to elemental composition of product ions enabling unambiguous interpretation of fragmentation trees not obtainable by the 3D-IT device (e.g. loss of isobaric neutrals). It should be emphasized that the types of product ions formed do not depend on the type of IT analyzer applied. For characterizing degradation products of antioxidants, the LIT-Orbitrap hybrid system, allowing the determination of accurate m/z values for product ions, is the method of choice.

A theoretical study of pure and mixed caesium clusters and cluster ions, CslHmO0/+n, l≤ 5: geometry, energetics and photofragmentation

Motivated by recent progress in the mass spectroscopy of the elementary reaction of alkali metals and water dispersed in ultracold helium nanodroplets (S. Müller et al., Phys. Rev. Lett., 2009, 102, 183401.), we investigate the properties of pure and mixed Cs clusters and cluster ions, Cs(l)H(m)O(n)(0/+), from a quantum chemical perspective. The presence of Cs atoms requires a careful choice of the methodology, which we have tested for small molecules for which experimental results were available. With the thus selected density functional, pseudopotential and basis set, we compute the geometry, the ionization potentials and the atomization energy, enabling a proper estimate of the energetics of cluster fragmentation upon photoionization. Based upon these calculations, we are able to construct a fragmentation tree that rationalizes the origin of all peaks observed in the experimental mass spectrum. Infrared spectra are computed, and we introduce a simple mixed quantum-classical model that essentially reproduces the cluster geometries.

Computing Fragmentation Trees from Tandem Mass Spectrometry Data

The structural elucidation of organic compounds in complex biofluids and tissues remains a significant analytical challenge. For mass spectrometry, the manual interpretation of collision-induced dissociation (CID) mass spectra is cumbersome and requires expert knowledge, as the fragmentation mechanisms of ions formed from small molecules are not completely understood. The automated identification of compounds is generally limited to searching in spectral libraries. Here, we present a method for interpreting the CID spectra of the organic compound's protonated ions by computing fragmentation trees that establish not only the molecular formula of the compound and all fragment ions but also the dependencies between fragment ions. This is an important step toward the automated identification of unknowns from the CID spectra of compounds that are not in any database.